WET

If you need to replay challenge levels in order to get this achievement, I recommend Chapter 10, "Shock Therapy." It's a very short level that can be played in 5 minutes, and more importantly, there is crossbow ammo in the level. You start out with 10 bolts, and there's a crate with 4 more on the second level right before the wall run ledge. Use 9 cleaning up the guys in the first room (both levels), and then pick up the all ammo box next to the health recharge, right before the elevator. That should top you off at 15 bolts (or, if you actually upgraded your ammo beyond that, you might want to save some more from the first room, since it's easier to get kills during the rage section).

Once you enter rage, camp out near a spawn door and take out the bad guys as they come out in pairs -- one bolt should get you both kills, and they're pretty much helpless right when they come out. If you're lucky you can get even more than that if you don't mind playing it more dangerously and letting them bunch up before you kill them.

Using this method you should be able to get 40 or more crossbow kills on each playthrough of the level. Once your crossbow ammo runs out you can switch to the sword if you still need that achievement, since this level works very well for acrobatic sword kills as well.

An easy way to get this is to play Chinatown Rundown on Points Count and kill every one with the Bow until you reach the first arena. Every time you get to a checkpoint load last checkpoint as this will give you 10 bow ammo. When you reach the arena quit and repeat.
20 Kills = 2:20 x 10 = 22 Minutes.