It seems that the reason why Shaggy is so unbelievably powerful in MultiVersus is that he ate a Gleamium rock, one of the main currencies used in the game.
One of the strangest things about MultiVersus (well, aside from watching Bugs Bunny kick the stuffing out of Superman) is that Shaggy is presented as an all-powerful being capable of taking on gods, riffing on the Ultra Instinct memes that released a few years ago. Although the real-world explanation behind Shaggy's power is likely because of those memes, it seems that there's an in-universe explanation as well.
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As pointed out by Twitter user reitheboi, Shaggy's bio on the MultiVersus website gives us a little insight into what he was doing before he found himself fighting the rest of the Warner Bros. library. According to the bio, Shaggy ate a "glowing crystal" that he thought was food, which then gave him incredible power. It seems that the crystal that Shaggy ate was actually Gleamium, one of the main currencies in MultiVersus.
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Shaggy's bio reads, "The last thing Shaggy remembers before The Change was exploring another spooky old mansion with his pal Scoob, just like any other day with the gang. He found a strange glowing crystal and, thinking it was rock candy, went to take a bite. There was a FLASH… and then blackness. When he came to, he found himself in possession of incredible powers."
After spotting the detail within Shaggy's bio, reitheboi tweeted about it, which was then tweeted by the game's director Tony Huynh, which is as close to an official confirmation as we're going to get. Who knew that MultiVersus would be providing essential Scooby-Doo lore?