Here is the full list of all 48 Street Fighter IV trophies - there are 35 bronze, 10 silver, 2 gold and 1 platinum.
Perform 100 Super Combos.
Perform 100 successful Focus Attacks.
Perform 100 Ultra Combos.
Perform 100 EX Special Moves.
Achieve 10 Perfect victories.
Perform 100 Special Moves.
Perform 10 Personal Actions.
Set your Title and Icon.
Win 1 ranked match.
Create 10 multiplayer lobbies.
Clear a Challenge in Challenge Mode.
Ruler of All
Unlock all characters.
Unlock all Colors.
Unlock all Personal Actions.
Collect all Titles.
Collect all Icons.
Perform 50 Super Combo finishes.
Perform 50 Ultra Combo finishes.
Perform 365 flashy background finishes.
Clear Arcade Mode with 1 character on Medium or higher difficulty.
Clear Arcade Mode with all characters on Medium or higher difficulty.
Clear Arcade Mode without using a single continue on Medium or higher difficulty.
Clear Arcade Mode on Hardest difficulty.
Defeat Gouken and clear Arcade Mode in Hardest difficulty.
Clear all Challenges in Challenge Mode.
Earn gold medals in all challenges.
Clear NORMAL Time Attack in Challenge Mode.
Cleared HARD Time Attack in Challenge Mode.
Clear NORMAL Survival in Challenge Mode.
Cleared HARD Survival in Challenge Mode.
Clear NORMAL Trial in Challenge Mode.
Cleared HARD Trial in Challenge Mode.
Collect all Medal types.
Collect 100 Medals.
Collect 500 Medals.
Collect 1,000 Medals.
Fight 10 opponents via fight requests.
Play 100 online battles. (ranked match or player match)
Play 200 online battles. (ranked match or player match)
Play 500 online battles. (ranked match or player match)
Win 5 online battles. (ranked match or player match)
Win 10 online battles. (ranked match or player match)
Win 50 online battles. (ranked match or player match)
Win 100 online battles. (ranked match or player match)
Win 3 ranked matches in a row.
Win 5 ranked matches in a row.
Win 10 ranked matches in a row.