This achievement takes place on the very first mission, the XM25 is your secondary weapon. From the start I would suggest trying to get as many kills as possible until you run out of ammo, later on the mission you will be asked to use this weapon to thin out the enemies. At which point your ammo will be restored. Not long after that section you will find an ammo crate which will restore your ammo for all weapons. Hopefully after the next room you would have killed enough people to get the achievement, if not then keep stocking up on ammo from the ammo crate.
I hope this solution helps you.