Guardian Diggers can tear into you with their claws, which is a really damaging attack. You will want to have a lot of PP for these Guardian Digger battles, but it's not easy to conserve PP while you go through the mines, because the enemies that hide out here are tough to defeat without PP. So, it's best to exit the mine, rest up and save the game after each Guardian Digger fight.

Use Flash to inflict a status ailment, and if you use Flash β or higher, there is a small chance that it will instantly kill the Guardian Digger.

Avoid using physical attacks on these foes (including bombs/bottle rockets/etc), because they start out having a power shield that will deflect physical attacks back at you. Use Jeff's Shield Killer if he has it, or just use only PSI if you have no way to destroy the shield.

Otherwise, focus on keeping everybody alive and patiently chipping away at Guardian Digger's HP with PSI attacks, and if you manage to destroy that shield or if it disappears on its own, use physical attacks.