He wants Tryndamere so he can gain his ability to resist death and his fury based power. Darkins can gain the powers and abilities of their hosts so I am thinking that Aatrox wants trynda to kill (his body) and pick up his weapon (real body) up so he can possess him. Rhaast gained Kayns shadow abilities if he gains full control over Kayn so it's not unreasonable to say that Aatrox wants more power, and that he can gain it through trynda.
I dig it, that's a pretty cool theory
doesn't want 
. It's actually the opposite.
want to kill for killing his entire tribe.
Already has his body and is content with his abilities, as he uses them for his artwork (Massacres). As one of the only surviving Darkin to not need to be resurrected from someone else he can easily be said to be the most cunning and strongest of the Darkin.
I would be down with your concept except that it makes Aatrox seem weak.
Tryndamere would probably make a really good host for Aatrox. That could be how they rework the Demonblade skin!
