To answer your question, Kama was still an Indian goddess when the Protagonist entered Ooku. She needed the Protagonist's love (and to 'love' him/her in return) to ascend into her full form, and she'd hooked herself up to the Palace of Ooku and made it her turf. She then plays around, knowing her antics will draw the Protag to her.
Now the Protag wasn't going to sit on his/her hands, so he/she starts exploring, finding clues and weird stuff around. This is all part of her plan, and she ascends without a hitch.
However, the Protag managed to turn bits of power from Ooku into an Anti-Ooku weapon, and when he/she hurts Kama with it (it's really just a bit more than a paper cut, but you know these types), Kama decides to disconnect herself from Ooku. This gives the Protag his/her chance, and he/she has an original inhabitant of Ooku become the new 'Owner', gaining Authority over the place.
Kama is forcibly expelled, and later defeated. She's already given and received Love from the Protag at this point, and this made it possible to summon her to the Protag as a Servant. It's heavily implied that she actually fell in love with him/her.
The story-related Challenge Quest (there's videos) are Kama with a gauge indicating how close to a full Beast she is. With a full gauge, she's a full-fledged Beast (grappling with the original inhabitant for control of Ooku), and that's actually the form just before she was defeated. It's one of the hardest Challenge Quests ever to be in the game.
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Not all the Beasts have been revealed at this point, so I'll just use the four I'm familiar with. Beast 666 (Beast VI The ***** of Babylon) has not had too many feats yet, so I'm leaving her out.
Here's a thought.
Assuming the Beasts are working together (a common enemy powerful enough to annihilate them seems enough motivation), they could very easily do this in round 3.
1) Goetia allows all the Beasts into his Temple of Time. I'm not sure if Tadano can brute-force his way in (only reason it could be accessed was because he brought it to his enemies to coordinate his invading Demon Pillars, and Chaldea reverse-engineered the connection), but even if he can, it'll take him a LONG time to even find it, and even long to break in.
2) Goetia uses his Clairvoyance and learns all about Tadano and how he came to be. Fou (Beast IV) uses his connection to Merlin to see Tadano's present, how he's transcended Time and Space and hunting them down).
3) Kiara and Kama, empowered by each other, prepares their most powerful abilities (they're the two sides of Beast III, and they still have all the powers a Beast would have, so working together will amplify that power a LOT).
A special Rule is invoked here--that your past made you who you are. It's actually why Kama, fully ascended (and thus transcending Time and Space to become her own Multiverse), could be hurt by the Anti-Ooku weapon (in this case, the 'starting point' of her Ascension). And any other Beast, for that matter.
Verse Equalization would make that Rule applicable to Tadano too. Thus he would retain all his past experiences up to the point he consumed the Cosmic Fruit, even if his 'current self' is transcendant.
4) With Fou's Authority, they force the concept of 'Human' on Past Tadano (because he struggled to get to where he is, overcame challenges and obstacles just like a human). Present Tadano is minimally affected.
5) Goetia uses Ars Almadel Salomonis to send them back to 'the Past' where they defeat and maybe kill Past Tadano, each one of them contributing to his defeat or death.
Back to the 'present', where they face Cosmic Fruit Tadano. With their 'past victory' against him, they use their Authority and carve the concept that [Tadano will lose to the Beasts] into Cosmic Fruit Tadano.
Then win, then cake.
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It's roundabout and convoluted and complicated, but this is most reliable way for the Beasts to win Round 3.
Round 1 could go either way, but Tadano would handily take Round 2.
