There are 49 Trophies that can be collected.

Bronze

Metropolis
Complete All Metropolis Story Challenges

Haven City
Complete All Haven City Story Challenges

Paris
Complete All Paris Story Challenges

Gleebertopia
Unlock The Final Gleebertopia Story Challenge

Fire In The Hole
Destroy 8 enemies with one grenade from the bouncer.

Lock N Load
Destroy 5 enemies with on Red Morphgun blast.

Simma Down
Complete a Haven City or Paris Challenge without overheating The Combuster.

Line Em Up
Destroy 3 enemies with a single melee attack.

Babysitting
Return 4 Whibblets simultaneously in a single Havey City or Paris Rescue Challenge.

Strike
Destroy 10 Pinbots with one ball detonation.

Chain Reaction
Save 4 Whibbles with one disc in a Haven City or Paris Jailbreak challenge.

Cool Whip
Destroy 8 enemies with one Whip Attack.

Just Enough
Get bronze medals on all story challenges.

Round of Applause
Get your first gold medal.

Look What I Found
Pick up your first hidden collectible.

Buckets of Bolts
Find all hidden gold bolts in Metropolis.

That's So Haven
Find all hidden precursor orbs in Haven City.

Pocket Change
Find all hidden coins in Paris.

Crystal Clear
Get a 30x Crystal Combo in Team Play.

25 is Alright
Get a 25x Multiplier

Day Care
Return every Whibblet simultaneously in a single Rescue Challenge.

Make It Look Easy
Save all Whibbles with one disc in a Haven City or Paris Jailbreak challenge.

Can't Touch This
Take no damage in a single Haven City or Paris Survival challenge.

Seen It All
Use every Ultimate Ability to dance with the Groovitron.

Dance Party
Get 200 total enemies to dance with the Groovitron.

In the Zoni
Destroy 200 total enemies via Zoni Attacks.

HaXxoR
Turn 200 total enemies against each other with Bently's Auto-Hack Ability.

Eco Power
Destroy 200 total enemies with Dark Jak's Eco Lightning.

Daxter's Whirlwind
Destroy 200 total enemies with Dark Daxter's Whirlwind Attack.

Sneak Attack
Destroy 200 total enemies during Sly's Thief Time.

Agorian Dishonor
Destroy 40 total Agorian Bombers.

Pork Chops
Destroy 100 total Boar Bodyguards.

Landfill
Destroy 2500 total enemies.

Party People
Earn 10 medals of any kind in Team Play.

Team Trauma
destroy any combination of 12 enemies or objects with One Team Strike.

Medic!
Give a teammate 20 Health Ups in one challenge in Team Play.

Spending Time With Friends
Give a teammate 10 total Time Extends in one challenge in Team Play.

Target Practice
Hit your teammate 100 times in one challenge with crystals in Team Play.

Ultimate Hero
Trigger your ultimate ability 3 times within one challenge.

Silver

The End
Complete Story mode.

1st Place Loser
Get silver medals on all Story challenges.

All Together Again
Find all hidden Gold Bolts, Precursor Orbs, and Coins.

50 is Nifty
Get a 50x Multiplier.

All Falls Down
Destroy 20 enemies during one Ultimate Ability activation.

Space Junk
Destroy 5000 totals enemies.

Gold

G.O.A.T.
Get gold medals on all Story challenges.

Diamonds are Forever
Earn gold medals on all Diamond challenges.

Nothing Up My Sleeves
Get a gold medal on a Diamond challenge without using an Ultimate Ability.

Platinum

PlayStation® Move Hero
Obtain all trophies.

http://www.ps3trophies.org/game/playstation-move-heroes/trophies/