Before fighting Ness's Nightmare, equip something that protects against Flash: ideally, the Night Pendant, Sea Pendant, or Star Pendant. If you don't have those, use the Earth Pendant that you bought here in Magicant.

Ness's Nightmare starts with a PSI Shield α. It makes it immune to PSI attacks (but without any deflection.) Ness's Nightmare can also cast Shield β, which will deflect physical attacks.

Otherwise, as long as you're protected from Flash, you just need to focus on staying alive. Ness's Nightmare can cast PSI Rockin α and PSI Rockin Ω. It can also heal itself up.

You'll be OK as long as you don't panic if you're mortally wounded. Just use lifeup on your next turn, and make sure that you recover PP before it runs out.

Use PSI attacks since Ness's Nightmare can't deflect them and can't put up another PSI Shield once its starting shield is gone. Otherwise, use things like Bags of Dragonite and Bombs.