Here is the full list of all 39 FIFA 13 trophies - there are 24 bronze, 11 silver, 3 gold and 1 platinum.
Unlock all other trophies (excluding additional content trophies)
Play 100 Head to Head Ranked Matches
Complete a match in every stadium
Play 5 consecutive Head to Head Ranked Matches without losing
Become a Legend as a player in Career Mode
Win consecutive League titles in any top tier League in Manager Mode
Win an online Friends League Match
Win a Tournament that starts with sixteen teams with a 1 Star rating team
Complete a Manager Mode Season without simming a game
Don't lose any matches played at Home in a season.
Score 50 goals using a touch shot
Win the Manager of the Month award in Career Mode
Get yourself selected in the Team of the Week in Career Mode
Score off the post or cross bar in a match
Play 5 consecutive matches without getting any cards (Bookings must be enabled in the settings)
Win a Created Tournament that starts with sixty four teams
Make 100 successful passes using the touchscreen
Chip the Keeper in a Head to Head Ranked match
Win a Head to Head Ranked Match using a weaker team
Sign a player better than anyone else on your club during the transfer window
Complete 5 Kit & Appearance Accomplishments
Win a Match with Manual Controls
Make 20 consecutive passes between at least 3 players in the opponent's half
Keep a clean sheet on World Class difficulty or higher
Unlock a trait for your Virtual Pro
Score a 90th minute winner in a game vs the CPU
Complete 5 Accomplishments that unlock Celebrations Packs
Score a Hat Trick with your Virtual Pro
Score a goal from a volley
Score a touchscreen or rear touch pad goal from a touchscreen pass
Create a Virtual Pro
Make a successful lob pass using the touchscreen in a match
Win a game when down one man before half-time.
Make a successful direct pass using the touchscreen
Make a successful through pass using the touchscreen
Score a penalty kick using a touch shot
Score within the first 5 minutes of the game in a game vs the CPU
Score a goal using the screen (touchscreen) shot, or a rear touch pad shot
Score a goal with a defender