I’d start by going through The Only Unfair Fight is the One you Lose posts:
Here, http://howtofightwrite.tumblr.com/post/52349151535/fight-write-the-only-unfair-fight-is-the-one-you-lose and here: http://howtofightwrite.tumblr.com/post/52428049557/fight-write-the-only-unfair-fight-is-the-one-you-lose
Beyond that, keep in mind, that for an assassin, they’re probably going to be killing any opponents as quickly as possible. Frequently, this means dispatching their foes before an actual fight can start.
If they do end up in combat, your character’s probably going to be looking for weapons to end a fight. If that’s a chair, lamp, toaster, or a handgun, then so be it.
I’m going to throw this one out there, since I don’t think we’ve mentioned it before: the head twist and break isn’t really a thing. Theoretically you can kill someone that way, but it takes a lot of force. And, from that position, it’s a lot easier (and quieter) to execute a choke hold and strangle someone to death that way.
Also, strangling someone takes a while. (And, no, this isn’t from personal experience.) Even after the victim goes limp, the character needs to keep choking them until the brain actually shuts down. Otherwise, they’ll just start breathing again, and recover.
I’d say look at Val Kilmer in Spartan and Tom Cruise in Collateral. Cruise is actually playing an assassin, while Kilmer is playing a government operative. It’s been a while since I’ve seen it, but the Thomas Jane Punisher film might also give you some ideas, there isn’t a lot of hand to hand, but that’s kind of the point.
If you have a lot of spare time, I’d recommend looking at 24. Kieffer Sutherland looks like he’s using a mix of Krav Maga and some miscellaneous CQB training. The problem is, there’s a lot of show (about 18 hours per season), and only a tiny fraction of that is combat.
There’s some good stuff in Burn Notice, so long as you remember that the only real difference between Michael and an assassin is that the latter is getting paid to kill someone. On the whole, the show is a good primer for tradecraft, which is useful for writing an assassin. Also, it’s entirely plausible to have an assassin that’s unwilling to kill people (outside of a contract), simply because it would draw more attention onto them, in which case, Michael is a very good character to look at.
Anyway, hope that helps.