There are 39 Trophies that can be collected.

BRONZE

Pinpoint Accuracy
Score a goal using the screen (touchscreen) shot, or a rear touch pad shot

Pressure is On
Score a penalty kick using a touch shot

You Pointing at Me?
Make a successful direct pass using the touchscreen

Thread the Needle
Make a successful through pass using the touchscreen

Control the Open Space
Make a successful lob pass using the touchscreen in a match

Nimble Fingers
Score a touchscreen or rear touch pad goal from a touchscreen pass

All My Own Work
Win a Match with Manual Controls

Against the Odds
Win a Head to Head Ranked Match using a weaker team

Good Week!
Get yourself selected in the Team of the Week in Career Mode

Great Month!
Win the Manager of the Month award in Career Mode

Woodwork and In!
Score off the post or cross bar in a match

In the Game
Create a Virtual Pro

Classy
Complete 5 Kit & Appearance Accomplishments

Trait-or
Unlock a trait for your Virtual Pro

Top of the League?
Win an online Friends League Match

Massive Signing
Sign a player better than anyone else on your club during the transfer window

FIFA Fair Play
Play 5 consecutive matches without getting any cards (Bookings must be enabled in the settings)

Tour Bus
Complete a match in every stadium

A Man Down
Win a game when down one man before half-time.

Don't Blink
Score within the first 5 minutes of the game in a game vs the CPU

No Draw for You!
Score a 90th minute winner in a game vs the CPU

Ruud boy
Score a goal from a volley

One Goal a Season
Score a goal with a defender

Defiance
Chip the Keeper in a Head to Head Ranked match

SILVER

Sharp Shooter
Score 50 goals using a touch shot

Pass Master
Make 100 successful passes using the touchscreen

Good Form
Play 5 consecutive Head to Head Ranked Matches without losing

Folklore
Become a Legend as a player in Career Mode

Challenging Schedule
Complete a Manager Mode Season without simming a game

Cup Upset
Win a Tournament that starts with sixteen teams with a 1 Star rating team

Custom Sixty Four Winner
Win a Created Tournament that starts with sixty four teams

Festive
Complete 5 Accomplishments that unlock Celebrations Packs

Tiki Taka
Make 20 consecutive passes between at least 3 players in the opponent's half

Sparkly Clean
Keep a clean sheet on World Class difficulty or higher

Off the Top of my Hat
Score a Hat Trick with your Virtual Pro

GOLD

Hundred and Counting
Play 100 Head to Head Ranked Matches

Back to Back
Win consecutive League titles in any top tier League in Manager Mode

Fortress
Don't lose any matches played at Home in a season.

PLATINUM

Football Legend
Unlock all other trophies (excluding additional content trophies)

http://www.ps3trophies.org/game/fifa-13-vita/trophies/