As the description states: Simply win one round of each game mode.
You DO NOT have to complete the full round. I joined a Defuse game approximately 30 seconds before it ended and just happened to be put on the winning team, and I still obtained the achievement.
The game modes are the following:
Conquest
Team Death Match
Obliteration
Rush
Squad Death Match
Domination
Defuse
This excludes the game modes: Air Superiority and Capture the Flag, as those are DLC game types. It will also exclude any future DLC game modes.
***EDIT*** If a game mode has an offense and defense side (such as rush) you do not have to win both sides.
Also, if you vote negatively please state why, so that I may improve on this, and future solutions.
***EDIT*** Credit goes to Rare Bishop: If you have already obtained this on the Xbox 360 version of the game, it will automatically unlock when you play your first match on the Xbox One.