There are 21 Trophies that can be collected.

Bronze

Puzzled?
Complete the first level.

Golden Boy
Get a gold rating on 5 levels.

Conquistador
Complete the first chapter.

Altitude Sickness
Complete the second chapter.

Bless you!
Complete the third chapter.

Great Adventurer
Complete the fourth chapter.

Eldorado
Get a gold rating on all chapter one story levels.

Because it's there
Get a gold rating on all chapter two story levels.

Howard Carter
Get a gold rating on all chapter three story levels.

Lost and Found
Get a gold rating on all chapter four story levels.

Master Puzzler
Get a gold rating on all levels.

Hoarder
Collect a total value of 250,000 in treasures.

Egyptologist
Get a score of 6,000 on the level Tomb of Osiris.

I see fish people
Meet the Agent.

Iced Out
Get a score of 8,000 on any level.

King of Bling
Get a score of 10,000 on any level.

Extracurricular Activity
Complete one of the optional levels.

Above and beyond
Get a gold rating on all optional levels.

Demolition
Defeat a Sentinel.

Innsmouth
Defeat an Agent.

Montgolfier
Scare Exocet.

http://www.ps3trophies.org/game/hamiltons-great-adventure/trophies/