Thonky.com's EarthBound Walkthrough

Everdred is an optional fight. Keep your HP at 50 or higher for this fight, because Everdred has some highly damaging attacks. It might be good to bring a Teddy Bear with you, because not only is Everdred kind of tough, but he sometimes tries to steal food from you. So it is not recommended to bring anything valuable with you. You can call Escargo Express to store your food or other items with them. If you have a Teddy Bear with you, Everdred might try to steal from the Teddy Bear instead of you, which helps protect your belongings.

Three PSI Rockin ɑs should be enough to defeat Everdred, although if you're unlucky, Everdred will attack on every turn, and that might be enough to inflict mortal damage on you.

The lowest level that you should attempt Everdred at is 8, but it will be tough at that level. At least level 9 is recommended. And don't go into this battle without the Copper Bracelet equipped.

After your victory over Everdred, he will tell you to look for Paula in Peaceful Rest Valley.