The_Imperator

They can rip entire worlds (meaning civilizations and their histories) completely out of the Web of Time, meaning it has no place in history any longer:

We can rip whole worlds from the Web of Time.

-Doom Coalition vol 1

They can also accelerate (and thus decelerate) entire solar systems (and larger spaces) through time with the push of a button:

CHANCELLOR: Of course they are. We can’t risk them getting hold of the weapon. The reports suggest they hit the Tenacity system with a reversal wave, yes?

AYMOR: I believe so, sir.

CHANCELLOR: Let’s see how they like the exact opposite. If we can’t have him, no one will.

...

(Big boom!)

BLISS: What was that?

DOCTOR: I don’t know, but I don’t like it.

OLLISTRA: They wouldn’t. They can’t.

DOCTOR: And that’s really steadied my nerves.

BLISS: Day, night, day, night.

QUARREN: The stars, the sun, they’re spinning.

OLLISTRA: They’ve accelerated the system. Hyper-evolution.

BLISS: What? What’s that?

DOCTOR: The usual progression of this planet has been sped up. We’ll experience thousands of years of development in moments.

RUPA: What, like continental drift, tectonic plates shifting?

DOCTOR: Exactly. This entire environment will change rapidly with every second that passes. We need to keep going.

BLISS: Can we still make it to the caves?

DOCTOR: I’m not sure the caves will even exist shortly.

OLLISTRA: They could become mountains, desert, even ocean.

DOCTOR: We need to find somewhere safe, somewhere stable.

...

OLLISTRA: Doctor, the sun.

DOCTOR: Yes, yes, I’d noticed.

BLISS: What about the sun?

DOCTOR: It’s getting older. Sooner or later it’ll go nova.

-One Life

They also have tech that attacks time lines directly, meaning it does not change time but attacks an entire time line as if said time line was a discrete length of "stuff" that can be interacted with:

DALEK: Analysis complete.

DOCTOR: And?

DALEK: This human was affected by chronon dispersal. Hypothesis, time disruptor weapons have been released on this world.

DOCTOR: That’s what I thought. Mind if I?

DALEK: Transferring data. (Into sonic screwdriver.)

DOCTOR: Yes, your readings show all the hallmarks of a particularly nasty form of attack. If I remember my Jane’s Guide to Time Weapons, they’re called Now Devourers.

BLISS: Now what?

DOCTOR: Temporal napalm. Microscopic organisms engineered to destroy the very concept of linear time. They must have been blasted all across this area, seeding instability. Jefferson was dragged into one of those battles we saw.

BLISS: Aren’t those battles from the past?

-Echoes of War

and more explanation:

RUPA: There was a rain forest out there. Jungle. I’m not certain, but I thought I saw movement in the trees before.

QUARREN: The whole area withered and died in moments. I’ve never seen anything like it.

DOCTOR: That’s what these readings are telling me. Everything in our immediate surroundings is suddenly in a constant state of flux. Bliss?

BLISS: The same. That was the Theseus falling out of hyperspace, or whatever was left of it, breaking apart in the atmosphere. But everything else is changing. Star maps, life signs. Is there something wrong with the scanners? Are they failing, shutting down?

QUARREN: Don’t look at me, I’m not the scientist. That’s my wife.

DOCTOR: Dalek technology is efficient, if nothing else. If that’s what it says, that’s what’s out there. Confusion. (Alarm.)

DOCTOR: Whoa, we’re losing it. I need to find something. (Alarm tails off and stops.)

JEFFERSON: Hey, it’s quiet out there now. Dead quiet.

DOCTOR: From what I can tell, the wave’s gone. It’s stable, for the moment. Stable confusion

...

QUARREN: The forest’s gone.

RUPA: No, it’s still here. Just withered, dried out and rotted. It’s like the trees have aged a thousand years in two minutes

-Echoes of War

The attack is not just affecting the planet, star charts are being altered meaning the entire galactic area is being rewritten by these things, chewed apart and spit back in random pieces by the Now Devourers. The end of the audio also reveals that this was the before-image of the weapons, like an after image but occurring "before" the weapons are activated, in a meta-time manner.

A description of the De-Mat gun, from The Book of the War:

A quantum computer linked to the causal nexus in much the same way as one of the Homeworld's timeships, the machine would scan its target and read the victim's complete timeline, then remodel everything else in creation without the target. The weapon didn't harm anything per se, but from an enemy's point of view being built out of molecules which the universe doesn't remember is harm enough. For the target there's no gap in the air in which to stand, no spare molecules to breathe, no history to demand action and no present in which to act.

Never-having-been is crueler than it may appear. The victim doesn't run screaming to his or her family's door, and never gets to see the mute incomprehension in their gazes. The victim has no hands. The victim has no eyes. He or she does, however, exist. The gun knows the victim: it had to, to cut the target out of causality. That precision requires knowledge of every particle which ever weaved its way through the target's body and that knowledge becomes indistinguishable from the particles themselves, once the data is detailed enough.

In essence, Time Lords have access to a weapon (multiple, as the War Doctor's last audio series revealed they built multiple to act as planetary defense measures) that literally rebuilds time around the target never existing. All molecules, components, energy, etc. that make the target up "currently", will make it up, and have made it up, never come into those positions. It's silly awesome hax.

In addition, to add to stuff like the Now Devourers, the Faction Paradox tech here in this match means that entirely new versions of enemies can be created as allies, simply by introducing a "paradox" into the past of the individual or group in question. The paradox doesn't even have to change much, just be a slight alteration in history, that a thing called a biodata virus piggy-backs on to eventually alter time enough to create a Faction loyal individual out of a future version of the target. It works on Time Lords, and on beings that are temporally protected, although for the latter case it needs a lot more work than just the above. However, given Time Lords are resistant to changes in their own pasts, it's not a strethc to imagine such a thing would work on things like Downstreamers or Xeelee or Photino Birds.

The Axis is where Time Lords stick time lines they don't like:

DOCTOR: Ah. It's rather as I feared. We're in the Axis.

PERI: The Axis?

DOCTOR: Yes. It's, er, a complex. Look, are you sure you want to hear this? We'll be on our way before

PERI: Doctor!

DOCTOR: Right, well, er, imagine the spokes of a bicycle wheel. Each spoke is a damaged or truncated reality, a sort of dead-end in Time. They're formed by changes in established history, some big, some relatively small, which cause the flow of subsequent events to spiral out of control. Often catastrophically.

PERI: And the Axis is the spindle, right?

DOCTOR: Exactly. The hub that maintains and regulates the truncated realities, and ensures that the contamination doesn't spread to the primary timeline.

ERIMEM: What?

DOCTOR: Oh. Well, it (sighs) It's like cauterising a wound to make sure the infection doesn't spread.

ERIMEM: Yes, I see.

DOCTOR: Now, if you'll excuse me (under the console) let's see about getting us out of here. Really don't want to hang around if we can help it. I'm sure if I just

PERI: Doctor.

DOCTOR: (out again) Yes, Peri?

PERI: How exactly do these timelines get er, damaged?

DOCTOR: Ah. Excellent question. And, well, though I'm ashamed to admit it, the answer can often be summed up in two simple words. Time Lords, who are, well-intentioned or otherwise, prone to dabble and not really tidy up after themselves.

PERI: So. This is all your mistakes tucked away in one big cupboard.

DOCTOR: Well, I probably wouldn't have put it quite like that, but yes, there's an element of accuracy in that description.

-Axis of Insanity

Basically, if the Time Lords don't like a time line, they send it into the Axis. The one the story is all about is one that was sent their after their agent, who was supposed to just clean up a mess, failed to realize the target had Time Lord level tech taken from another universe. The Time Lords just disconnected his entire time line from reality and shoved it into a box. Other time lines accessible from the Axis are a bunch of alternate Gallifreys, that feature in the audio series Gallifrey. Most of the series, in fact, is about alternate Gallifreys in the Axis.

Time Lords use their Eye of Harmony to alter reality as they see fit, enforcing the physics and histories that they want:

Gallifrey, and it's Eye of Harmony, grants almost infinite power. The Matrix accesses to a vast view of space-time, to see where it may be deployed, and through the time vortex we make our projections reality.

- Songs of Love (Doomsday Coalition 4)

This is further reinforced thanks to the Doctor's replica EoH, which decidedly does not give as much power as the normal one seeing as he runs low on power, has enough temporal energy to link every point in space/time to an exploding TARDIS:

In a far future event the TARDIS explodes and the Eye of Harmony within it causes temporal energy to burn at every point in time and space simultaneously. Cracks begin to appear and some are big enough for whole planets to fall through.

The light pouring out the cracks carrries so much temporal power that it wipes from existence anything it touches-so species across the universe come together to lock up the Doctor and prevent this event from ever happening.

-The Visual Dictionary

the comic Wormwood shows that a Time Lord robot, with access to a copy of the EoH, could completely rewrite physics everywhere at once.

So in sum, the Time Lords enforce their version of history by laying out a Web of Time, which effects everywhere at once thanks to the EoH. In the words of Lawrence Miles in Book of the War, they are the species responsible "for engineering history". History is constantly reinforced by them with the web of time, which, while it can be broken by time travelers that know where to hit, is resilient enough that most attempts to change it simply cause alternate time lines to form rather than collapses.

But even ignoring the Web, in this case Time Lords are basically resistant to changes to their own time line as a civilization.

From the RPG, a description of the Transduction Barrier:

This ancient device bent space-time around

Gallifrey in a manner that essentially locked it in

its own space-time continuum. Direct transport

to Gallifrey or through the space around it was

only possible by use of a TARDIS or by following

a homing signal provided by Gallifrey Space

Control. Anyone else entering the Transduction

area would find their paths diverted in much the

same manner as the path of light is distorted by

the extreme gravitational lensing of a black hole.

Basically, it locks Gallifrey into its own spatio-temporal bubble with only access being through the Time Vortex. It isn't always completely opaque the surrounding space/time, though, as it has to normally be set to full power (some quotes from the audio Neverland):

"Gallifrey has been sealed off ever since the time distortions began to warp the weft of reality, yes?"

"Anti-time cannot pass the transduction barriers which separate Gallifrey's continuity from the remainder of space-time. You're temporal locks are too strong."

"Not one single atom can arrive on Gallifrey without authorization, that's true."

Time Lord Transduction Barriers have been shown to be resistant to all temporal weapons and items the Gallifreyans can bring to bear, as the Daleks had the exact same system as the Time Lords and were thus unable to be erased.

And when Time Lords are directly involved in events, time changes take a "while" to actually come into effect:

VIOLA: What do you think, Doctor? About Shakespeare.

DOCTOR: I think he was the most accomplished, talented and influential playwright who ever drew breath. I think his prose is peerless, his sonnets sensational, and his blank verse beguiling.

LEARMAN: Got some sense in that head of yours then.

DOCTOR: I think his disappearance from history is a symptom of something far more dangerous and insidious. A fracture in Time itself.

LEARMAN: But if Time itself has changed, how can we be aware of it?

DOCTOR: Thus far, Shakespeare's removal from history is only a possibility, but it's rapidly becoming a probability. As the chance of it really happening increases, so more people forget.

CHARLEY: And as that becomes more probable, so it becomes more tangible?

DOCTOR: Mmm, but the main event that will cause it hasn't happened yet. It's just a possible event for the moment, becoming inexorably more certain with every second that passes.

LEARMAN: But what enterprise of such pith and moment could have that effect.

DOCTOR: I don't know. But it will happen soon and it will happen here. It's interesting that you don't immediately dismiss my suggestion as utter nonsense.

-The Time of the Daleks

Basically, any attempts to manipulate time are easily fixable or noticeable by the Time Lords.