Here is the full list of all 10 Claws of Furry trophies - there are 7 bronze, 1 silver and 2 gold.
Beat the boss of Junktown!
Beat the boss of the Sewers!
Beat the boss of the City!
Beat the final boss!
Last in the Arena for 10 waves
Unlock all outfits
Kill 100 Enemies
Uppercut 100 Enemies
Use your Bullet attack on 100 Enemies
Finish the Tutorial