--Hoodlum's Havoc (GBA)--
2 Fists
Body slam
Golden fist
--Hoodlum's Revenge--
Heavy Metal Fist
--Rayman 1--
Fast fist
Gold fist
Super fist
--Rayman 2--
Woods of Light shot
Fairy Glade shot
Canopy shot
Golden fist
Robound 1
Rebound 2
Rate of Fire
Accumulation 1
Accumulation 2
Dogfight - Well, I don't know what you mean by Dogfight, so can you explain it a bit?
Energy sphere (Crow's Nest)
--Hoodlum's Havoc--
Vortex
Heavy Metal Fist
Lockjaw
Shock Rocket
Shooting Vehicle (at the TOTL) - You mean the underwater part? That's correct, although I meant something else (but your answer is good enough)
Big feet
Rayman shoe
--Hoodlum's Havoc (GBA)--
2 Fists
Kicking off ledges - You don't get the power to hang on ledges and thus to kick with your feet, right? On the other hand, special conditions have to be met before you can kick with your feet, but that could also be said for normal punching with fists...Since the other 2 are probably good, this one is wrong.

Besides, the correct answer is very easy to find.
Golden fist
--Hoodlum's Revenge--
Heavy Metal Fist