Recommended Level: 80+
If you’ve unlocked the Special Training in the SOP Shop, you can fight Gardino at Granzalk Garrison Post. (Talk to the soldier on the left side of the reception desk.) I recommend waiting until you’re at least level 80 - but even then, you may have to fight him a couple times before you win.
- drop Fossil Plate
Use Fortify right away, and keep using it whenever it wears off, and you can probably win this battle regardless of your level.
If you prefer more of a challenge, then I would recommend using Ragnazeilast and trying to keep everyone else alive while Ryle uses Brave Force to refill the Deadliness Gauge.
Gardino uses Break, Slash, Tear in this battle (and Ogresmash!), and it will most likely kill at least one party member each time he uses it. Just Revive them as necessary.
Since this is a total bonus boss battle, and one that's intended to be a real challenge (I assume), I'm not going to provide a detailed strategy for beating Gardino. (Anyway, by this stage in the game, you should know what everyone's strongest skills are.)
I will note, however, that you may need to use the occasional Spilrau in this battle, to give Rumil a turn to use Healing Wind before Gardino attacks.
The final reward for defeating Gardino is a Tupsimati - and, you can earn more than one.