There are 37 Trophies that can be earned in this title.

Bronze

Puppeteer
Create a fighter in Create A Fighter

Puppetmaster
Win a fight against the CPU with a fighter you've created in Create A Fighter

As Real As It Gets
Experience an entire 8 fight event card in Event Mode.

White Belt
Win 10 Online Exhibition matches in total

Baby Steps
Win an Online Exhibition Ranked match

Warriors, Come Out And Play
Join an Online Camp

Under Your Wing
Act as a trainer in Online Camp Training

Submission Technician
Win a fight with a Submission Transition

It's The Jits!
Win a fight by Submission against a non-CAF, Expert CPU in the first 60 seconds of Round 1.

Steamroller
Win a fight by KO/TKO against a non-CAF, Expert CPU in the first 60 seconds of Round 1.

Kay. Tee. Eff. Oh!
Win a fight by Flash KO against a CPU opponent.

Learned Student
Go through all tutorials

Tournament Title Holder
Win at least one championship in the Tournament Mode

Testing the Waters
Play all modes at least once, check the shop and all options

Honorable Fighter
Touch gloves at the beginning of 10 matches.

Coming Up Next…
Download an Event for Event Mode

Blog Fodder
Complete a post-fight interview in Career Mode

Silver

Hot Hands
Win 10 Online Exhibition Ranked matches consecutively

Olympic Mixed Martial Artist
Online Exhibition – Obtain all types of gold medals

Gotta Catch 'Em All
Collect all Topps UFC Trading Cards

Veteran Champion
Complete the Title Defense Mode

Budding Champion
Complete the Title Mode

Ultimate Unlocks
Complete all A, B, and C class challenges (Red and Blue Corner) in a fight in Ultimate Fights Mode.

Yellow Belt
Win 25 Online Ranked Matches

Purple Belt
Win 50 Online Ranked Matches

Brown Belt
Win 75 Online Ranked Matches

The Cessation Sensation!
Win by all methods of stoppage against the CPU. (KO, TKO, Submission, Doctor Stoppage)

Bobbin' And Weavin'
Dodge 3 consecutive strikes via sway (Outside of Tutorial Mode)

Move Mastery
Reach 'World Class' (Level 3) status with a technique or move.

Gold

Hall of Famer
Compete in a Champion vs. Champion fight and also make the UFC Hall of Fame in Career Mode

So Now You're A Fighter
Complete the Career Mode

Pound For Pound Champ
Win a Champion vs. Champion fight in Career Mode

Black Belt
Win 100 Online Ranked Matches

Platinum

Platinum
Congratulations!

3 Secret

http://www.ps3trophies.org/game/ufc-undisputed-2010/trophies/