You won't be able to complete this until you gain access to the Airship and find Omega Ruins. You get Nova by using Lancet on Omega Weapon. If you have already defeated Omega, your only other option is Nemesis which requires you to capture 10 of every fiend for the Monster Arena and defeat all the other creations.
If you didn't learn any other abilities until you got the Airship, you can easily get them all as you go about capturing all those fiends. Fire Breath and Self-Destruct in Mihen (Dual Horn and Bomb) Stone Breath in Djose (Basilisk) Aqua Breath in Macalania (Chimera) Bad Breath in Calm Lands (Malboro) Doom in Cavern of Stolen Fayth (Ghost) White Wind and Mighty Guard on Gagazet (Dark Flan and Behemoth) Thrust Kick in Zanarkand Dome (YKT-11)