Trip World (1992) is an aptly named game developed by Sunsoft, a video game company you might know by titles like Gimmick!, Ufouria and Journey to Silius.
It follows a rabbit-like creature called Yacopu on his quest to retrieve a flower and his kidnapped girlfriend so that peace will return to his world. Along the way he gains abilities including turning into a ball and a big, scary godzilla-like rabbit.