This is in an entire session, not just one kill. This is actually very easy to obtain, especially at higher levels and if you are familiar with the previous Assassin's Creed Brotherhood multiplayer. This can be obtained at level 1 if you wanted. An easy mode to get this in is Steal the Artifact. You can gain a lot of points by obtaining the artifact and hiding with it in a haystack. You will see people (such as first place in the match) gain upwards of 5000+ points. Even if almost last place you can pull off the 2505.
Note: Before unlocking the achievement, it quotes as saying 2500 points. After obtaining the achievement, it then says 2505 points. You must get 2505 for the achievement, not 2500.