Here is the full list of all 12 Sonic the Fighters trophies - there are 7 bronze, 4 silver and 1 gold.
Fight a mirror match in Arcade Mode or Offline Versus
Complete Stage 7 of Arcade Mode (any difficulty)
Complete Stage 6 of Arcade Mode (any difficulty)
Complete Stage 5 of Arcade Mode (any difficulty)
Complete Stage 4 of Arcade Mode (any difficulty)
Complete Stage 3 of Arcade Mode (any difficulty)
Complete Stage 2 of Arcade Mode (any difficulty)
Destroy all of an opponent's barriers while playing Arcade Mode or Offline Versus
Complete Stage 1 of Arcade Mode (any difficulty)
Win a round without receiving any damage in Arcade Mode (any difficulty)
Turn small by being attacked (ie, by Amy's↓+P, etc) in Arcade Mode or Offline Versus
Use Honey the Cat in Arcade Mode or Offline Versus (Press START button on Amy and select)