It is not known to evolve into or from any other Pokémon, despite its close resemblance to Goomy. However, while GigaGoomy is known to have formerly existed as CyberGoomy, it is not known if it became GigaGoomy through evolution or if it was artificially modified for more power.
No method exists to legitimately obtain GigaGoomy in-game.
GigaGoomy appears once in-game as a Pokémon used by Elite Four member Wilson in the Challenge Championship. Not much is known about GigaGoomy aside from what was described by Sir_Willis_CMS in the data given from the "Hall of Masters Laboratory Records":
Gigagoomy, the banchou. Formerly CyberGoomy, GigaGoomy has managed to overcome all limitations through use of an energy as of yet unknown, but nicknamed 'spiral energy' by researchers. Despite the danger, Wilson was unafraid of the monster and it has since become the prize of his team.
Because GigaGoomy cannot be obtained by the player, it is not possible to obtain a full list of the moves it is capable of learning. However, there are a few moves that are known from the player's Challenge Championship battle with Wilson.