How do I complete the Montreal mission without killing any guards?

I assume you're talking about the part where they've dispatched many Belltower agents who are on constant alert. I found that liberally abusing the vents allowed me to get to areas where they weren't as dense, or weren't able to spot me while I was flanking them. I did it with very little cloaking, although I also had the tranq sniper rifle and quite a few darts.

Even if there are two together, you can usually shoot one, reload, and shoot the other before he has a chance to alert other guards or wake the first guard up.

If you can, try to move the sleeping guards quickly into an area where none are patrolling, although this can get tricky in some of the more dense areas. Going cover to cover and avoiding them altogether might be a better strategy in certain parts. This was one part of the game where I found it tricky to employ a "no witnesses" strategy without resorting to murder.

If you get stuck, cloaking can be a useful strategy. Make sure you check the various rooms to find additional power restoring food to keep your cloak and melee takedown energy full.