An anime with a badass character who is mad/obsessed with killing or at least fighting...

Yuno Gasai from Mirai Nikki is obsessed with Yukiteru, therefore turning her jealousy and protectiveness into violent and psychopathic tendencies! She's not a character I'd want to cross paths with, hahaha

fighting...i guess Black Rock Shooter and Kagari is..crazy obsessed with Yomi at high Yandere levels

Samurai Deeper Kyo has a main character with dual personalities, one docile and another murderous.

I think I have a girl who fits all three a little to well. Roberta from Black Lagoon and Black Lagoon Ova: Robertas blood trail. From completely beating someones face until only the lover jaw is left, to biting a knife into pieces with her jaws, to starting a war with the U.S. military all by herself to even chewing on Ritalin like candy to also de-chaining a chainsaw with two pistols... I mean come on. <-- Obviously she is not someone you want to anger. She's otherwise known as The Bloodhound of Florencia or The Terminator Maid. Armed with a spas-12 shotgun disguised as an umbrella, a machine gun suit case, a ton of grenades and ammo and spiked brass knuckles as well as a Flintlock Rifle and Metal Poles along with two Colt .45 pistols( I believe that's what they were) a grenade launcher , and a .50 caliber sniper rifle that she shoots with one hand. ( Sigh )