Deadliest Warrior Battlegrounds

This must be obtained by any one class. It is not accumulative across all classes. You can check your progress by looking under Profile and selecting your designated class. The kills are listed in top left (crossed swords icon). This also gets you progress towards getting to Rank 25 for one of the classes, which is needed for the Grand Master achievements. You also need 100 kills in each of the six classes for the Master achievements.

For getting kills, I found it easiest to pick one map and stick with it (The Moor by default) so you can memorize spawns. You then can choose 11 bots to go after in FFA (slayer-type game). Each match lasts 15 minutes, and I averaged around 60-80 kills per match while using melee weapons for faster kills. Any two-handed weapon also kills people faster. That means about 15 matches x 15 minutes for a total of about 4 hours of grinding for kills.

The achievement will pop the instant you get your 1000th kill with that character class during a match.