There are 40 Trophies that can be collected.

Bronze

Betilla's Back!
Head Nymph Betilla is Free!

Beautiful Beats!
Holly Luya, the Music Nymph is Free!

Feed the Fairy!
Edith Up, the Gourmet Fairy is Free!

Merm-Aid!
Annetta Fish, the Ocean Nymph is Free!

Nymphs Rock!
Helena Handbasket, the Mountain Nymph is Free!

Scout
You found 10 hidden cages.

Speedy!
Earned 5 speed trophies!

Electoon Friend
Completed 10 Medallions.

Milk Tooth
Earned 1 Skull Tooth.

The Bubblizer!
Chain-Bubblized 4 Enemies.

I'm Back!
Replayed any completed map.

Painless!
Completed a level without taking a hit!

Vacuum Snack!
Inhaled 50 things on Moskito-back.

No Panic!
Saved ALL Darktooned Wizards in 'Port 'O Panic'.

B Side!
Played an Unlocked Character in any map.

Hover Happy!
One hour of flight time!

Crusher!
Crushed 50 Enemies.

Crush Combo!
Simultaneously crushed 4 enemies.

Sprinter!
Sprinted a Marathon!

Fisher King!
Swam a Marathon!

Kung Fu Combo!
Perform a swipe-to-air Kick Combo!

Hyperspeed!
Sprinted for an Entire Level!

Boing! Boing! Boing!
Bounce-Bubblized 11 Enemies without landing in 'Polar Pursuit!'

Survivor!
Survived a Piranha Pond without a scratch!

Back At You!
You Bubblized a Hunter with his own live missile!

Clear Sighted
You found 30 Relics.

Bubble Wrap Maniac!
Popped 100 Item Bubbles with tap.

Grim Reaper
Popped 50 Enemy Bubbles with tap.

Silver

Explorer
You found 25 hidden cages.

Turbo!
Earned 15 speed trophies!

Electoon Hero
Completed 25 Medallions.

Full Mouth
Earned 5 Skull Teeth.

Blue Baron!
Beat the Giant Eel within 60 Seconds in 'Aim for the Eel.'

Eagle Eyed
You found all Relics.

Gold

Dr. Lividstone, I presume?
You found ALL hidden cages.

Nitro!
Earned ALL speed trophies!

Electoon Legend
Completed ALL Medallions.

The Jaw!
Earned ALL Skull Teeth.

Platinum

Sweet Dreams!
Won ALL trophies in the game! SICK!

1 Secret

http://www.ps3trophies.com/forums/playstation-trophy-news/12630-rayman-origins-trophy-list.html