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Background
There's no fistfight tournament going on in this act, but you can always go and practice with Roche's boys over in their camp.
Walkthrough
This quest starts once you talk to Mette at
#1. You'll learn that they're practicing for hours every day, but Geralt points out that they didn't improve a whole lot. As such, they'll challenge you to a fistfight match.
Your first opponent in the row is Fenn. Hit your QTEs in the right moment and he's down in no time. Next contender is Silas. He's slightly tougher than Fenn, but again fist fights aren't exactly challenging. Once he's defeated, Roche will come and try to interrupt your streak, wondering why you're fighting his men. Then he'll challenge you to a fist fight. Roche isn't much different from the others, except that he can take more hits.
After you defeat Roche, the quest
Against the Blue Stripes ends. Then a soldier from Kaedweni camp, Burton, will come and taunt you into fighting him, saying that he's tough compared to the Blue Stripes commandos.
Depending on your win or loss, you'll open up a new quest for Act III called
A Score to Settle. Simply beat the soldier like the others and you'll start the quest. After the battle Zyvik will come and chase the Kaedweni away because he meddled in fistfights. Burton says that the fight isn't over and warns you not to look for square coins (related to the main quest Conspiracy Theory).
1 - Roche's camp, Mette, Silas, Fenn, Roche, Burton