Breathedge

Once youve restored the Normandys weapons by completing the first docking station you arrive at, (where you have to build the dome) you'll be able to start killing coffins. Killing coffin robots will calibrate the weapons and raise their lvl.

First thing is to get the ship repaired. A little ways from the ship you docked at, there is an auto repair station. It's got a big blue glow and white exterior.

Once you've done that, continue a little bit away from the docking station until you see a red health bar show up. This is what spawns coffins. It will continually spawn them until it's destroyed. For the purpose of this achievement (and as a by product the Undertaker achievement for killing coffins) we don't want to destroy it yet.

What your looking for is a red circle coming towards you. The safest way is to creep up until you see ONE circle coming for you and back up a little. This stops you from getting swarmed. Start firing as soon as you see the circle. It's easy to hit them when they are coming right at you from this angle. If they zip past, try to back up from the spawning station and try to shoot it down but if you don't, it will just head back to the spawn point. They don't regain health.

If your taking too much damage, you can always head back to the auto repair. Do this if you reach half health. They will follow you quite a ways when your heading back and are accurate so don't wait too long.

There's no progress meter and I didn't keep count but it was A LOT of kills to get to lvl 4. It gets easier as you go since your damage goes up with each lvl.

If you keep a safe distance and try to get them one at a time, you'll get it easy. Tedious but easy.