Bradley killed a man in the ring.
It's established that Bradley was a boxer, but he expresses no interest in returning to the ring. This, coupled with his seemingly-inhuman strength, makes it possible that he killed someone in the ring and is ashamed of it. Backed up by his Tranquil Fury tendencies; he constantly tries to keep himself under control even when fighting. And, finally, it would also explain as he possibly ended up in Gil's debt. Bradley was consciously taking it easy on the first guard he fought.
The first guard that Bradley fights appears to give him a tougher challenge than pretty much anyone else. While the man was admittedly a boxing coach, it's not explained why this medium-security guard is so much tougher to defeat than the guards at Red Leaf. The answer, possibly, is that Bradley didn't want to outright maul him. Not only did he just get the news of what he needs to do, but the guard had very recently apologized for his earlier behavior, something Bradley would likely respect. Both of these factors combine to mean that Bradley wasn't fighting with nearly as much zeal as letter on. He did snap the man's arm, but that seemed more out of necessity than anything else. Bradley is an ex-Marine (and probably an Iraq War vet).
I don't know, he just has that vibe to him. You need to have met Marines and war vets to know what I'm talking about. He shaves his head, he alludes to a dark and gritty past, a lot of criminals are ex-military, Bradley is very patriotic, Marines are known for their boxing, and he clearly has a long history of killing people.