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