In the original game this was a reward for having a complete Twisted Metal Black save on your memory card.
Luckily they're not paywalling trophies behind other games just yet and this is available right from the start.
Every monster has 2 skins available to begin with, with the exception of Agamo who has 1, 2 and 4 unlocked. Start a match as Agamo with skin 4 and the trophy will unlock.