When I play spy, it always seems that when I have to go to my gun, it's always a desperate situation. I have a real hard time getting head-shots under pressure, and I can't imagine willingly trading in damage and firing speed. What is a play style for the Spy that will allow me to effectively use the Ambassador?
The play style to take advantage of the Ambassador is something like a behind-enemy-lines sniper. The best way to think about is is as a long-range back stab, since it requires precision to use effectively, but when you are successful, you will take down enemies very quickly.
Ambassador = alternatives
Per usual, your goal as a Spy is to sneak behind your enemies. Normally, your next goal, apart from sapping the Engineer's structures, would be to get in position to back stab your enemies, but with the Ambassador, you have the option of trying to get in a few quick head shots instead, which lets you attack your enemies from further behind than normal, allowing you to play more cautiously than normal as well.
Ambassador vs Revolver
Since the Ambassador emphasizes head shots, and since head shots are easier to get on enemies who are unaware of your presence, the Ambassador is more suited for initiating conflict in situations where a back stab attempt is unfeasible or risky, such as when you come across a sniper equipped with the Razorback, or a Pyro. It would be better thought of as a weapon suited for 'back-of-the-head' shots rather than one simply suited for head shots.
The basic Revolver is more suited to ending conflict by finishing off survivors of failed back stab attempts, or holding off enemies who are pursuing you. Also, since it is normally more powerful than the Ambassador, it is also better for finishing off the Engineer's structures, especially after you have begin sapping them.
If you are successful at sneaking behind enemy lines but have difficulty in getting up close for back stabs, the Ambassador can be an effective alternative.
Ambassador goes very well with the Cloak and Dagger, allowing you to find the perfect hiding spot and take your time with lining up a headshot, or waiting for an enemy to walk into your field of vision.
Trying to get a headshot while fleeing with a Dead Ringer or under time-pressure with your normal cloak watch is much less effective.
Become the Sniper Spy.
It is true that as a panic defence, the Ambassador is less effective than the default pistol, unless you got a very good aim. But it does open up new strategies, mainly to dispatch unsuspecting enemies at distance. A fair alternative, if you can't get into the knife range. Also snipers with the Razorback.
There is one trick you can pull with the Ambassador against tanking engineers that isn't realy viable by other means. If you can't get to the engineer by normal means, or it's too risky, seek out a place where you see both the engineer and the sentry that is outside the sentry's range. Pull out the Ambassador, snipe the engineer (should take one or two head shots) and then shoot the sentry.
You have to remeber, if you wait a couple of seconds between shots, the Ambassador is 100% accurate in relation to the crosshair. You'll know when you can make an accurate shot, when the crosshair stops shrinking.
For me, the best time to use the Ambassador is on snipers with the Razorback. Since your knife becomes essentially useless on a Sniper with a Razorback, the ambassador is a great alternative. Since the sniper is likely to be standing still, thinking the shield will protect him, it's quite easy to get a solid headshot on the first shot, and a body shot will usually finish him on the second shot.