From the Super Mario Wiki
Giga Bowser is the final boss of Adventure mode in Super Smash Bros. Melee. As his name suggests, he is a gigantic version of Bowser, and can only be fought after completing Adventure Mode in normal or higher difficulty within 18 minutes without using any continues. In the cutscene that follows when the player accomplishes this, Giga Bowser is created when a Bowser trophy falls onto the Final Destination stage, and is then immediately struck by lightning, right after the player defeats the giant Bowser. This revives the trophy, but the energy surge from the lightning causes the strange mutation that turns Bowser into Giga Bowser. Defeating Giga Bowser in Adventure Mode awards the player 100,000 points, along with the Giga Bowser trophy. Additionally, he is one of the opponents in the final Event Match; The Showdown, with Ganondorf and Mewtwo fighting alongside him.
Giga Bowser returns in Super Smash Bros. Brawl as Bowser's Final Smash. Many of Bowser's moves are hugely powered up in this form, and his roar is deeper. However, some of his attacks are actually weaker than that of the regular Bowser (such as the forward smash). He still takes damage from hits, but he won't flinch, making him possible to KO only by hitting him when off-screen, and at the top border of the screen. Giga Bowser's Super Smash Bros. Brawl trophy incorrectly states that he can't take damage at all. Because of his large size, Giga Bowser is able to easily attack and KO an opponent. The duration of this move is very short.
Giga Bowser also appears as Bowser's Final Smash in Super Smash Bros. for Nintendo 3DS / Wii U, but while Bowser's moveset has been altered, Giga Bowser maintains his moveset from Super Smash Bros. Brawl.
Giga Bowser is officially considered to be a Super Smash Bros. character, and not a Mario character. In the game, his icon is not a mushroom (as is the case with Mario characters), but a Super Smash Bros. symbol (as is the case with Super Smash Bros. characters). In Super Smash Bros. Brawl and Super Smash Bros. for Nintendo 3DS / Wii U, Bowser's Final Smash has a mushroom icon, but this is because it is a move of Bowser's, and not a separate entity like the Giga Bowser in Super Smash Bros. Melee.
In addition to being much larger than the original king of the Koopas, Giga Bowser looks far more ferocious, with a larger body, a spikier scaled shell, more muscular physique, and a new curve to his lengthened horns. As well as being an intimidating sight to behold, Giga Bowser is far more difficult to battle than his smaller counterpart.
Powers and abilities
Giga Bowser possesses the same moveset as Bowser, but several moves have an elemental effect; for example, his down smash can freeze opponents, and his forward smash is explosive. However, unlike Bowser, Giga Bowser does not have a swim animation; when Giga Bowser jumps into the water, he falls right through it and gets KO'd. Giga Bowser also cannot pick up items, but he can still possess the effects of the Bunny Hood and Superspicy Curry through Special Brawl.
Names in other languages