There are 27 Trophies that can be collected.

Bronze

Tune in
Tune in Complete the Trophy Level for Tune In

Dyadic
Complete the Trophy Level for Dyadic

Magic Circle
Complete the Trophy Level for Magic Circle

Traids
Complete the Trophy Level for Traids

KKKKKKKKKKKKK
Complete the Trophy Level for KKKKKKKKKKKKK

Giraffes? Giraffes! In Outer Space
Complete the Trophy Level for Giraffes? Giraffes! In Outer Space

Silver

Admirable Virtues
Complete the Trophy Level for Admirable Virtues

Line 'Em Up!
Complete the Trophy Level for Line 'Em Up!

It's Steam Engine Time
Complete the Trophy Level for It's Steam Engine Time

Match Sprint
Complete the Trophy Level for Match Sprint

A Heroic Dose
Complete the Trophy Level for A Heroic Dose

Observations on the Beautiful and the Sublime
Complete the Trophy Level for Observations on the Beautiful and the Sublime

Expansion
Complete the Trophy Level

Morphic Resonance
Complete the Trophy Level for Morphic Resonance

Play for 18 Triads
Complete the Trophy Level for Play for 18 Triads

Not Playing is Becoming Increasingly Oppressive
Complete the Trophy Level for Not Playing is Becoming Increasingly Oppressive

Just Take a Pinch
Complete the Trophy Level for Just Take a Pinch

Winds of the Dawn that is My Crown
Complete the Trophy Level for Winds of the Dawn that is My Crown

Becoming Purple
Complete the Trophy Level for Becoming Purple

I Really Missed Jack
Complete the Trophy Level for I Really Misesd Jack

Gold

Danger
Complete the Trophy Level for Danger

The Light Spectrum
Complete the Trophy Level for The Light Spectrum

Miracles
Complete the Trophy Level for Miracles

A Subliminal Reprise
Complete the Trophy Level for A Subliminal Reprise

Perpetuation
Complete the Trophy Level for Perpetuation

The Jupiter Mission
Complete the Trophy Level for The Jupiter Mission

Platinum

Peking Duck
Successfully completed all 26 Trophy Levels

http://www.ps3trophies.com/forums/playstation-trophy-news/19408-dyad-trophy-list.html