You have a 50% chance of success with PSI Flash against Plague Rat of Doom, and if you have PSI Flash γ or PSI Flash Ω, you have a reasonable chance of a one-hit kill. If you don't get it within two or three turns, though, you might not want to bother with it.

The Plague Rat of Doom likes to inflict poison on your allies, so you might want to bring some healing items with you so that you can focus your PSI efforts on attacks instead of healing.

In general, don't wait to heal your allies. The Rat is tough, so you could find yourself in a lot of trouble very quickly.

The Plague Rat of Doom will do SMAAAASH attacks half of the time. Therefore, a physical deflection shield like Shield β or Shield Ω might be helpful.

Try some Big Bottle Rockets, and consider having Ness put a shield around Poo.