She uses these forms one at a time to defeat the Beastkin Mother, the Elf Mother, and the Succubus Mother in the tournament, since their racial traits give them specific advantages against Mamako in the competitions at hand. She turns into a Loli when she gets cursed by Amante and Sorella and it brings her nothing but downside, but Porta is eventually able to craft an antidote.
Hahako later uses a mixture of the Beastkin, Elf and Succubus transformations during her final match against Mamako to bring herself all the advantages (She's described as simultaneously having Cat Ears, Elf Ears, Devil Horns, Succubus Wings, and a Cat Tail). Later, when Hahako snaps and reveals her true form as an amorphous, ethereal lovecraftian horror with hundreds of tentacles and clawed reaching arms, she's so she's able to shapeshift her individual hands so that each of them transform into a Hahako with a specific transformation, so that not even a combined assault from all the mothers in the tournament are able to overpower her.
Hahako is truly the most powerful character in the series so far by a long shot. Makes me wonder how strong Hahades is going to be when we get to Vol. 8.