The T-Rex's Bat (Godzilla Bat in Mother 2) is a weapon in EarthBound. It can be bought for $698 at the Winters Drugstore and sold for $349. It increases Ness's offense by 48 and can miss by 1/16 of the time. Like all bats in EarthBound, this item can only be equipped by Ness.
Initially when Jeff is playable in Winters, he seemingly can't purchase the bat as he only has a few dollars in cash and doesn't carry an ATM Card like Ness. However, it is possible to sell the Broken Spray Can that Jeff starts with as well as the items enemies drop in order to build the cash necessary to buy it. Doing so will give Ness a decent power boost early on, but it will take some time and luck to gather the funds.