If Jeff has any bottle rockets, use one on his first turn, and have Ness use his strongest PSI Rockin. This might be enough to defeat Dept Store Spook on on the first turn. If not, keep hitting it with bottle rockets.

You might want to have Ness only use PSI Rockin once, at the beginning of the battle, and then conserve PP for healing after that.

Dept. Store Spook can use PSI Freeze, Brainshock, Lifeup, and Magnet. Ness will be unable to use a shield for protection, because his shields only block physical damage. You have a 50% chance of success with PSI Flash and PSI Sleep.

It would be wise to bring a Teddy Bear with you, although if you have one before Paula's kidnapping, it might get destroyed by other enemies before you can reach Dept Store Spook, so try bringing several.

Make sure Jeff has some Horns of Life or other revive-from-death items in case Ness bites the dust. Otherwise, Ness is going to have to focus a lot of effort on keeping himself and Jeff healed up throughout the battle.