Here is the full list of all 27 Dyad achievements.
Complete the Trophy Level for Play for 18 Triads
Complete the Trophy Level for Expansion
Complete the Trophy Level for Match Sprint
Complete the Trophy Level for The Light Spectrum
Complete the Trophy Level for Line 'Em Up!
Complete the Trophy Level for Admirable Virtues
Complete the Trophy Level for Magic Circle
Complete the Trophy Level for Tune In
Complete the Trophy Level for Danger
Complete the Trophy Level for Dyadic
Complete the Trophy Level for It's Steam Engine Time
Complete the Trophy Level for A Heroic Dose
Complete the Trophy Level for Observations of the Beautiful and the Sublime
Complete the Trophy Level for Morphic Resonance
Complete the Trophy Level for Triads
Complete the Trophy Level for Miracles
Complete the Trophy Level for Not Playing is Becoming Increasingly Oppressive
Complete the Trophy Level for KKKKKKKKKKKKK
Complete the Trophy Level for Just Take a Pinch
Complete the Trophy Level for Winds of the Dawn That is My Crown
Complete the Trophy Level for Becoming Purple
Complete the Trophy Level for Giraffes? Giraffes! In Outer Space
Complete the Trophy Level for I Really Missed Jack
Complete the Trophy Level for A Subliminal Reprise
Complete the Trophy Level for Perpetuation
Complete the Trophy Level for The Jupiter Mission
Complete all 26 Trophy Levels