Thonky.com's EarthBound Walkthrough

Bring your Jar of Fly Honey into this battle. Unless you use the Hungry HP-Sucker, this fight will be impossible without the fly honey. Belch is invulnerable to everything but the Hungry HP-Sucker if you don't use the Jar of Fly Honey on him. After using the fly honey on Master Belch, he will rarely attack.

To end the battle quickly, just use Bottle Rockets and Ness and Paula's best PSI. Belch is highly vulnerable to sleep, but it's hardly necessary if he's eating the fly honey.

When you get rid of Master Belch, you can go through the door behind him to get back to Saturn Valley. There, you will be able to reach Milky Well.