I'll think of a spiffy introductory passage later.
Blue Beetle #1: A completely inexperienced Jaime with no idea about how to use his powers fights Guy Gardner. His shields block Guy's attacks for a while before he eventually loses.
Blue Beetle #2: Telepathic resistance; a telepath named Probe tries to scan Jaime but the scarab fries her mind.
Blue Beetle #3: Moves fast enough to block several energy bursts from hitting their target after they were fired.
Blue Beetle #4: Fights some magic tree monsters; his scarab detects their magic energy trail and figures out how to stop them.
Blue Beetle #7: Dodges energy attacks from several OMAC's (although one hits him), and later destroys all the OMAC's with one blast.
Blue Beetle #14: Fires an energy attack at Guy Gardner that cracks his shield a little.
Blue Beetle #14: If Jaime is blinded, incapacitated or killed, the scarab is capable of independent action.
Blue Beetle #16: Short-circuits a spell from Eclipso, but the backlash knocks him out for a while.
Blue Beetle #17: Endures a lightning bolt and tornado from Typhoon.
Blue Beetle #17: Defeats Typhoon.
Blue Beetle #18: Produces kryptonite radiation to hurt Supergirl, and then gets tied up by Wonder Girl. It wasn't a serious fight.
Blue Beetle #18: Takes a hit from Lobo, it knocks the wind out of him for a while but he gets back up and enters the fight again.
Blue Beetle #18: Endures the heat of a rocket launch.
Blue Beetle #19: Defeats Giganta via nerve strikes.
No seriously, nerve strikes.
Blue Beetle #21: KO's a large group of people with one non-lethal blast.
Blue Beetle #21: Fights the Spectre and accomplishes absolutely nothing. He creates an anti-magic bubble, the Spectre walks out and shuts down his systems with one touch. That was all the fight consisted of. I posted this simply because I have seen people on the battle forums claim that Jaime has weapons that can hurt the Spectre; he does not. I do not know where or how people got it into their heads that Jaime can harm the Spectre.
Blue Beetle #26: Fights and defeats Parasite. I have no idea what's happening here since this was a special all-Spanish issue, but from what I gather Parasite tried to drain the scarab but it backfired and triggered some kind of transformation into the scarab's full Infiltrator mode, and then he got his ass kicked.
Blue Beetle #33-34: The scarab temporarily shuts down Jaime's body, playing possum to save him from a potentially lethal attack from Dr. Polaris.
Blue Beetle #34: Defeats Dr. Polaris by negating his magnetic powers, albeit with some help.
Teen Titans #52: Gets blitzed by Bart Allen from the Titans Tomorrow future, and then creates an energy shields that fries Bart when he tries to phase through it.
Titans #17: Shield tanks a hit from Cinderblock (who in that same story was strong enough to knock around Bombshell and Miss Martian).
The Brave and the Bold #3: Endures a blizzard.
Supergirl #62: X-ray, sonar and sonics.
Booster Gold #21: Beats up a giant killer robot called Thinko. Has a tactical nuke at his disposal.
Booster Gold #22: Tricks a group of killer robots into killing each other by messing with their targeting mechanism.
Booster Gold #22: Can levitate people.
Booster Gold #24: Fights the Black Beetle, and creates a tachyon field to prevent him from time-traveling.
Booster Gold #25: While temporarily evil, creates a gun that can blow up the planet (according to him) and outraces a nuke.
Justice League: Generation Lost #3: Restrains multiple OMAC's in a magnetic force-field that could last for 17 years.
Justice League: Generation Lost #19-22: Max Lord builds an energy weapon that damages the scarab, and then shoots Jaime in the head. The scarab heals him from seeming death.
Justice League: Generation Lost #24: Defeats OMAC Prime by tricking it into absorbing the power of the scarab, and then corrupting it by controlling the portion of the scarab that it absorbed.
Blue Beetle #2: Resists Phobia's telepathy.
Blue Beetle #2: The armor is bulletproof and has mini-taser....beetle....things.....
Blue Beetle #4: Neural scrambler.
Blue Beetle #7: Hacks an ATM.
Blue Beetle #7: Can see invisible people.
Blue Beetle #7: Can hit intangible people. The writer must hate Martian Manhunter or something.
Blue Beetle #9: Fights Kyle Rayner and Bleez. He temporarily freezes Bleez and then dodges Kyle's attacks for a while until the GL's attention is diverted by a bounty hunter sniping him in the back. Then Bleez gets back in the fight and Jaime gets a boner or something.
Blue Beetle #10: Incapacitated by the DEO frying him with a Khund weapon. When he wakes, he breaks free by short-circuiting the entire building.
Blue Beetle #11: Fights Booster Gold. They go at it for a while until Booster eventually gets the upper hand, but Jaime gets some help......
Blue Beetle #12: Rematch with Blood Beetle. He cures Paco by conducting some impromptu heart surgery. Something like that is not really applicable in a whole lot of scenarios, but it's a good example of how the scarab can come up with a plan and update Jaime on what to do in a second.