Crocodile girl is her!
Vector the Crocodile (Sonic the hedgehog): Most fondly, and as a sea creature she often gets paid by the Sea Queen, Cordila Guinevere. Also Kail's a hungry eater, and swims like a real crocodile
Kazuichi Soda (Danganronpa 2: Goodbye Despair): I know that Soda has a beanie, but during later chapters Kail wears a beanie...probably
Gaz membrane (Invader Zim): Childhood! Gaz as a heacanon voice is fits with Kail! Rough/tomboy voice, plays games, gets annoyed and mad.
King K. Rool (Donkey Kong): For Starters, her right eye has a scratch, so comically her left eye would be wider.
Killer Croc (DC Comics: I always dream of Kail turning into killer croc, but then that Idea Hit me 'If she can turn into a Croc beast, then she will be Partial'
Kagura (Azumanga Daioh): Kagura is a tanned girl as in Tropes word 'she puts fiery passion into anything she does, her hot-blooded exterior hides a tender heart' That Idea makes it wonderful for Kail, like she's a rage girl but also nice and sometimes reads books