One after another the opponents will try and kill him off. Punisher knows about these guys, their tactics, weapons etc and they know about him too. Both the Punisher and his next enemy get 12 hours prep time before the next confrontation. He's fully rested after each fight.
You're giving the mercs the same amount of prep? Ummm, that's not good for Frank. His prep is usually good enough to get him a leg up on street levelers, but some of these guys outclass him up front. Given like prep, they'll outclass him 2 days later. He stops at round 1.
Round 1: Bests Jason by staying at a range and using his superior marksmanship to grab a win. He'll stock up on explosives during his prep (harder to dodge a blast radius), as well as some device he can use to track the former Robin to prevent stealth.
Round 2: He does the opposite to Floyd, sneaking up on him and wrecking the assassin in hand to hand.
Round 3: Same as above, but instead of fist fighting Bullseye he'll just put a bullet in his head when he's not looking.
Round 4 n' 5: I DUNNO LOL
Round 6: Goads Wade into a trap. This shouldn't be out of the question considering Frank's intelligence and Deadpool's... Deadpoolness.
Round 7: Same as above. Taskmaster is a cocky jobber, so it should be even easier to lure him into a trap than it was Deadpool.