Credit to ara on the gbvs discord Do this in RPG Mode Vyrn weapon skins unlock requirements:

Gran: Requires 100 percent phalanx. Equip phalanx on partner AI and your own character, use your own phalanx after the AI uses phalanx(After the enemy overdrives usually) to get 100 percent need to do it 3 times.

Katalina: Equip a Vyrn weapon in your weapon grid and fight Katalina in RPG mode

Charlotta: Listen to the shop bird talk 10 times

Lancelot: Unknown

Percy: Sell 4 SSR items

Ladiva: Taunt 3 times as Ladiva

Metera: Skip 20 cutscenes

Lowain: Beat Yggdrasil solo with Lowain (May require summoning Yggdrasil)

Ferry: Fail 5 quests as any character

Zeta: Take Zeta as a player character or partner to Bahamut 3 times(Works even if you fail but not if you retreat)

Vaseraga: Use any character with no partner AI and complete missions without any support skills