This achievement is cumulative.
The 500 kills part is fairly self-explanatory--get 500 kills. The kills count in any ranked versus game mode, but it is hard to find a game with enough players to launch. You need to have at least a 2-on-2 lobby for the game to launch in team modes, so it's most likely something you'll need to boost these days.
Objective points are awarded for, you guessed it, completing objectives in ranked matches.
Capturing a flag, capturing a territory, and killing the enemy flag carrier are all worth one objective point.
Capture the flag probably works best for this. Capture flags like a madman and kill flag carriers like a fiend, and you'll get this in no time.