The training area is ripe for picking off surprisingly easy achievements, and this is no exception. You can get a handful of achievements by grinding the area at the beginning of the game. Here's how:
Start a new campaign (or choose Somalia from the Missions menu and play as Salem) and turn the difficulty to Recruit. Now go through Aggro Training. There's a Heavy halfway through that's incredibly easy to beat with all the surroundings on easy. Takes me about two minutes to get to him each time, so rinse and repeat to fill your 25 kill quota.
A few other achievements you can get with this include:
Very easy to get with your standard assault rifle. You'll get it while playing normally, but you can also get it by replaying this mission.
They teach you how to do this, and all the enemies are incredibly weak. Rinse and repeat to get this easily as well. All kills rack up on your weapon, too.
At the first cover spot, you can just keep firing and get this. Probably the easiest achievement here.
When you're asked to swap your primary with Rios, switch to your secondary. He'll give you a Scorpion in return, which you can use to rack up SMG kills.