I'm looking for mangas with a cool (cold, emotionless, aloof...) heroine who doesn't wants to separate with and/or is very/only fond of the hero. She can be clingy, possessive or just very attached to the male lead, but important is that her personality fits a 'cool' description.
I prefer shounen and seinen with not too much comedy but I don't mind shojos and joseis.
Thank you

hmmm,
what you'll find in seinen will most likelly bring out some echi...
i'll try to throw some withouth echi... and with a strong heroine:
(also note that there is gore in most seinen)

Dorohedoro
Kamiyadori
Majin Devil
Negative Happy Chain Saw Edge
Re:Birth - The Lunatic Taker *****
Saitama Chainsaw Shoujo
Shut Hell
Variante
Elfen Lied
Aflame Inferno
Kimera *******
Pupa
Otoyomegatari
Superior *******

Second Witchcraft Works.

You could also try:
Kandachime, Clockwork Planet, Shiki Tsukai

More comedic ones:
Choku!, Baketeriya

this is an old one but Shaman King kinda fits your description

Thank you all!
I look through them

I was sure someone would have said this but
Shingeki no Kyojin