Neither is more correct. Both sentences are equally correct.
Everybody holds hands. That is a fact, that means everyone is holding someone else's hands, it is not a complete sentence. You would need to say "everybody holds hands at the concert" for example.
Everybody hold hands. That is a command, that is someone telling everyone else that they must hold hands. This one is a complete sentence and is fine by itself, the other one is correct when it is part of a complete sentence, even though technically it is correct by itself it may not make a lot of sense.