This secret achievement is called Spider Hunter and is awarded for killing 12,000 spider-type insects. Spiders look like...well, spiders. There's a picture below for reference.
This will most likely come naturally if you are playing for the completion, but if you need to grind it, or just want to get it out of the way, the best mission for this is Level 52 - Bug Invasion. There are about 200 spiders in this mission and no other enemies, so it's fast and easy.
You can check your progress in the Battle History tab from the mission preparation screen.
The achievement will pop immediately upon killing the 12,000th spider.
NOTE REGARDING KILL COUNTS:
Both online and offline kills will count toward your kill counts for any of the "Kill X number of Y enemy type" achievements. If you die and restart the level, or even if you die and exit the level, your kills will still count, although you will lose any armor and weapons that you picked up.Thanks to WileyOldFox for the info that Bug Invasion is Level 56 in online mode.