Captain Claw -- All Eight Bosses Defeated Without Losing Health

Sometimes I start with less than 100hp, but no hp is lost in the boss fights themselves.
1. Le Raux. When he's backed against a wall he slides forward and stabs you. Just keep him away from walls and spam high slash attacks.
2. Katherine. One of the hardest bosses for this type of challenge. Like LeRaux, keep her in the middle of the arena. If she gets close to a wall she uses her cartwheel attack.
3. Wolvington. Get in close ASAP. If he starts spamming magic attacks you'll definitely take damage. The idea behind the pistol shots is to distract him so that he can't do that. When close, alternate between hitting him and ducking his return slash, his patterns are predictable.
4. Gabriel. Pretty hard. I got lucky when I was playing him. I narrowly missed bombs twice, and barely avoided mid-air collision with a Red Tail Guard.
5. Marrow. LONG. Be wary of mental fatigue. The parrot can be hit with a sword or bullets (the advantage of using a sword is that it doesn't cause Marrow to start shooting back at you), I used bullets for this one.
6. Aquatis. Really easy. There's no unpredictability, you just go ahead and execute a strategy. Zuczek throws dynamite from the shore, and that's probably the better way, but I'm used to throwing from the brick so that's what I did here.
7. Red Tail. Kind of a luck based fight. If he throws knives down at you you'll get hurt, if he uses his wind power you'll get hurt, if he does neither of those things you can get up on the platform, jump like crazy, and pray. I nearly take damage at the end. He whips out his pistol and is a frame or two away from shooting when I land that final blow.
8. Omar. So many things are trying to hurt you, and it's long as hell. I have the 1.3 patch which means Omar takes 4 hits to kill (instead of 8 or 10 or whatever). Pistol shots will distract him and stop him firing magic blasts.