Play style
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.

Summary
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.

Play style
The play style to take advantage of the Ambassador is something like a behind-enemy-lines sniper. The best way to think about it is as a long-range backstab, 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 backstab 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 an Engineer's buildings, especially after you have began sapping them.

Summary
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.