There are 50 Trophies that can be earned in this title.

Bronze

Meet Gine
Win the challenge 'Meet Gino'.

Pocket money
Win the challenge 'Pockey money'.

Seed capital
Win the challenge 'Seed capital'.

Impress Nikolai
Win the challenge 'Impress Nikolai'.

One half of the treasure
Win the challenge 'One half of the treasure'.

Rookie Cup
Win the challenge 'Rookie Cup'.

Motion Cup
Win the challenge 'Motion Cup'.

Good company
Win the challenge 'Good company'.

Access all areas
Win the challenge 'Access all areas'.

Record Breaker
Win the challenge 'Record breaker'.

Perfect 10
Win the challenge 'Perfect 10'.

In a hurry
Win the challenge 'In a hurry'.

Dislike of prime numbers
Win the challenge 'Dislike of prime numbers'.

Narrow path
Win the challenge 'Narrow path'.

Two's company, three's a crowd
Win the challenge 'Two's company, three's a crowd'.

Roadblock
Win the challenge 'Roadblock'.

Last Chance
Win the challenge 'Last chance'.

Stumble and win
Win the challenge 'Stumble and win'.

Reserved
Win the challenge 'Reserved'.

Torpedo
Win the challenge 'Torpedo'.

Belly flopper
Win the challenge 'Belly flopper'.

Flawless flight
Win the challenge 'Flawless flight'.

International emergency call
Win the challenge 'International emergency call'.

Counting up
Win the challenge 'Counting up'.

Counting down
Win the challenge 'Counting down'.

Maximum airtime
Win the challenge 'Maximum airtime'.

Jolly jumping 1
Win the challenge 'Jolly jumping 1'.

Jolly jumping 2
Win the challenge 'Jolly jumping 2'.

Jolly jumping 3
Win the challenge 'Jolly jumping 3'.

Almost untouchable
Win the challenge 'Almost untouchable'.

Lucky strikes
Win the challenge 'Lucky strikes'.

Counterstrike
Win the challenge 'Counterstrike'.

Silver

Greedy
Win the challenge 'Greedy'.

In shape without training
Win the challenge 'In shape without training'.

Prosperity
Win the challenge 'Prosperity'.

Fabulous wealth
Win the challenge 'Fabulous wealth'.

Impress Stacy
Win the challenge 'Impress Stacy'.

Gold obsession
Win the challenge 'Gold obsession'.

Cosmos Cup
Win the challenge 'Cosmos Cup'.

Destiny Cup
Win the challenge 'Destiny Cup'.

One on One
Win the challenge 'One on One'.

Couldn't care less about Marc
Win the challenge 'Couldn't care less about Marc'.

World domination
Win the challenge 'World domination'.

First try
Win the challenge 'First try'.

Choose wisely
Win the challenge 'Choose wisely'.

Bad posture
Win the challenge 'Bad posture'.

Ultimate body control
Win the challenge 'Ultimate body control'.

Flawless victory
Win the challenge 'Flawless victory'.

Gold

I've got the power
Win the challenge 'I've got the power'.

Platinum

Platinum Trophy
Won all Trophies.

http://www.ps3trophies.org/game/summer-challenge/trophies/