Young Ryu
Flame: Automatically gained after meeting Nina in the Wyndian dungeon.
Defender: Automatically gained after escaping from Sunder at Mt. Boumore.
Reverse: At the [?] spot south of Mt. Boumore.
Thorn: Behind a tree at Momo's rocket crash site near the Tower.
Frost: Near the house below the bridge at the Maekyss Gorge.
Thunder: Behind the [?] hut in the northeastern Rhapala region.
Eldritch: At the top of the Lighthouse near Rhapala.
Miracle: Inside Mt. Zublo.

Adult Ryu
Shadow: Automatically gained after defeating the Dragon Zombie.
Fusion: Automatically gained after defeating the Dragon Zombie.
Force: In the Underground Laboratory at the Plant.
Gross: In the Tidal Caves.
???: In the [?] hut west of Steel Beach.
Mutant: Along the shore at Steel Beach.
Trance: At the Yggdrasil tree's grove in the Lost Shore region.
Failure: At the Colony.
Radiance: In the Alcove near the portal at the Container Yard.
Infinity: Automatically gained after defeating the Elder.

Strongest Dragon Forms
Whelp: Gross
Dragon: Element + Defender
Behemoth: Thorn + Miracle
Mammoth: Miracle + ???
Trygon: Flame+Frost+Thunder
Warrior: Gross + Force
Myrmidon: Force + Trance
Pygmy: Mutant + ???
Tiamat: Trance + Shadow
Wildfire: Miracle + Thorn + Reverse
Super Rei Hybrid: Fusion + Force
Super Nina Hybrid: Fusion + Eldritch
Super Momo Hybrid: Fusion + ???
Super Peco Hybrid: Fusion + Shadow
Kaiser: Infinity + Radiance + Trance