BioShock 2

Enter into the prologue to set up your classes, then enter the lobby to join into a match. Get into a position where you're comfortable with your ability to get a kill and fire before the opponent can see you so you can get the kill. Pops up immediately afterward.

Kill your first person in any online multiplayer match setting. Should be quite easy.
Since you start off with the pistol and shotgun, I recommend a shotgun to use for your first few kills.

Get a Kill in a public match easy...Achievement Unlocked!

This was the first achievement I unlocked for the game! This achievement is easy to obtain if you're familiar with the play style of the game. The easiest way to get a kill is with a plasmid-gun combo. Charge up the Electro Bolt in your left hand and when you see an enemy unleash it. It'll do some damage and paralyze the enemy for a the moment, then unload on them with either your starting pistol for short/med range or shotgun for in-your-face range. Also researching already dead enemies will give you a damage boost for a greater chance of victory! When you do kill your first enemy you'll be granted the achievement worth 10G!

The following video is of my first online Bioshock 2 game. If you follow my written guide and take my playing style into account you'll be killing more than your 1st kill for this achievement!