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