Here is the full list of all 23 SkyScrappers (EU) trophies - there are 6 bronze, 9 silver, 7 gold and 1 platinum.
Obtain all other trophies
Complete a four-player multiplayer game with all human players
Complete all the single player campaigns
Complete the single player campaign as Kichirou
Complete the single player campaign as Jessica
Do a special move jump
Complete the single player campaign as Solene
Win a game by landing on the roof of a building
Win a game without losing any health
Complete the single player campaign as Phileas
Do a vertical rush trick
Strike a flaming object into another character
Do a special move attack
Completely fill your super bar
Hit an opponent with a ground pround attack
Do a long jump trick
Do a three point landing trick
Win a match for the first time
Strike a falling object into another character
Do a slide trick
Finish a game with a weapon attack
Win your first round
Do a jump of over 15m from an inclined platform