Battle Strategy
This is a relatively easy boss fight. The Electro Specter fights alone. The first thing to do is before the battle. If you have it, put the Franklin Badge on your weakest member. Once you enter battle, the Electro Specter will use Jeff's Neutralizer and Shield Killer. Use this time to do any necessary healing. Don't bother with Shields. They'll waste your time. If you have Multi-Bottle Rockets, feel free to use them, although it's not necessary.
Have Ness attack or use Bombs. Paula should use PSI Freeze Ω. Jeff should use the Heavy Bazooka or variations of Bottle Rockets. Have Poo use his highest level of PSI Freeze, which is likely γ. The Specter should fall easily.
This strategy assumes you have these items. Have Paula use her most powerful level of PSI Freeze and Jeff should use items. If not, he should attack, obviously.