This is my build to solo the Isolation Vaults (this might also be good for a team running the Isolation Vaults).

Phase 1 use Mallet and Amp to draw the enemies' attention away from the mixer and use Metronome for invisibility.

Phase 2 do the same thing as in Phase 1 to kill enemies and stay invisible.

Phase 3 do the same thing but in case it's not enough, have a gunblade like the [Stropha] or [Redeemer] (Prime if you have it) and build it for heavy attacks, radiation, crit chance and have [Corrupt Charge] on it and it'll usually be enough to one or two shot the Necramech(s) in the vault.

The bonus phase (if you want to do it for both the tier 1 and 2 vaults, and I recommend you do it for the tier 3 vault) use Mallet first then Resonator (this part might not be necessary but it's what I did) to make sure the enemies don't go for Loid and Otak and Metronome for (do I really need to repeat this one?) invisibility.