There are 48 Trophies that can be collected.

Bronze

Motion Master
Complete a race steering with the motion sensor function.

Air Assault
Punch a fellow rider off their bike or ATV while you're both in mid-air.

Hot Air
Use in-air cooling to entirely cool your full Boost gauge from Critical in a single jump.

I Made it Myself
Modify your vehicle using all the available options.

Energy Efficient
Win a race without ever entering Critical Boost.

Target
Ram and wreck the same opponent twice during a race.

Kudos
Earn 250 chips from a single drift in Multiplayer.

Variety is the Spice of Life
Complete a race in all of the standard game modes.

Pure as Mud
Successfully perform 3 stunts in a single race.

Wheelin' and Dealin'
Pull a continuous wheelie for 5 seconds.

Unlucky for Some
Win a race with each of the 13 vehicle classes.

FPR
Win a race using only the vehicle-mounted camera.

Grease Monkey
Swap out at least one vehicle part on each of the 13 vehicle classes.

Over There!
"Look At" 5 unique race incidents over 5 different races.

Rampage!
Use the Ram to wreck 10 opponents.

Found One!
Collect 1 of the hidden MotorStrom Cards.

'You Wanna Play?'
Make it to the party as Mash.

'We're gonna race – in that?'
Complete 'Off the Rails' as Mash.

'Eat my dust, tough guy!'
Complete 'Aces High' as Mash.

'Okay, let's do this'
Complete 'Credit Crunch' as Mash.

'You wanna stay, shut your mouth'
Make to the party as Tyler.

'I'm just waiting for a sucker to beat.'
Complete 'Road Warriors' as Tyler.

'I'm all in.'
Complete 'Suburban Shakedown' as Tyler.

'It's about life and death.'
Complete 'End of the Line' as Tyler.

'Only one of us is making it out of this city alive.'
Complete 'The End is Nigh' as Tyler.

'Restricted my ass!'
Start the party as Big Dog.

'Time to lose these guys…'
Complete 'High Way' as Big Dog.

'If you start, you get to finish…'
Complete 'Final Drive' as Big Dog.

Now fo the Main Event…
Pass 5 Special Events.

Starter for 10
Pass 10 Special Events.

Gently Does It
Complete your first online race.

Where's My Money?
Place and win a bet in Matchmaking.

High Five!
Reach Rank 5 in Multiplayer.

Stacked
Reach Rank 15 in Multiplayer.

Where Do You Put Them All?
Earn 50 Accolades in Multiplayer.

Decorated Stormer
Earn 25 Medals in Multiplayer.

Silver

Found 'em All
Collect 150 of the hidden MotorStorm Cards.

'Want a Magic Nut Bar?'
Complete 'Baked' as Mash.

'And Mash Wins!'
Survive the Festival as Mash.

'I guess you love trouble…'
Complete 'Wargames' as Tyler.

'Any Questions?'
Complete 'Sea Spray' as Big Dog.

Nail'd It
Pass 25 Special Events.

Double or Quits?
Win a bet while on a 2x Hot Streak.

Croupier
Reach Rank 30 in Multiplayer.

Gold

'We're the best… it's that simple.'
Survive the Festival as Tyler.

'You're Greased.'
End the Festival as Big Dog.

Jackpot
Reach Rank 40 in Multiplayer.

Platinum

The Big One
Obtain every other trophy in the game.

http://www.ps3trophies.com/forums/trophy-news/56583-motorstorm-apocalypse-trophy-list.html