You can customize your character with gears and status that amplifying your shield damaging skills like Shield Boomerang, Rapid Smithing, Shield Charge, Reflect Shield, Shield Spell, Earth Drive, Shield Press, Shield Spell and Reflect Damage.
For example you'll want shield that's quite heavy and one that provide specific skill modifier boost like Cross shield for cheap Rapid smithing and Shield Boomerang boost.
or
Gearing yourself with tons of autocast gears both physical & magic for Reflect focused shield build through shield reflect/reflect damage skills
or
Default Heavy category shields like Imperial guard (slotted & 250 Weight) /Giant Shield (slotted & 280 Weight) /Royal Guard Shield (slotted & 300 Weight) /Bunker Shield (not slotted but 350 Weight) for Every shield skills usage that rely on Shield Weight as its main damaging formula.
You can use above heavy category shields under constantly synthesized shield / FCP effects with Alchemist/Biochemist/Genetic Slave for unbreakable properties or default slotted sacred mission for innate unbreakable properties with less damaging potential.
AFAIK we don't have card that give shields unbreakable properties yet, CMIIW though if anyone here might knows