if Prime is strong enough to shatter reality with his fists
He was only able to do so from the pocket dimension he was residing in, and because he was a denizen of Earth-Prime, the reality in which DC's writers existed, thus he could manipulate events just like the writers.
Well, if it's COIE Anti-Monitor, he's a multiverse buster so that's pretty obvious, and the only way that Superboy Prime "beat" Anti-Monitor was when he had a planet smashed onto him, and had the guardians fighting him. Should be a stomp.
Superboy Prime took the same damage the AM took War World and Guardians he wasn't hurt at all.
You're assuming he did, but he wasn't in the panel of War World exploding; only the Cyborg and the Anti-Monitor were.