**** SPOILER ALERT ****
This achievement is obtained in a second after you kill the final boss - 'Subject 88'.
Capture all the areas of the map (there are 20 of them) by finishing available missions, and eventually you will face the 'Change of plans. It's Subject 88, we must eliminate him' message or so.
You then will be faced with a tough guy with a long-range rifle.
You can try to kill him, but I would recommend to obtain all of the weapons and buy all available upgrades before trying that.
The simpliest tactics is to fastly deploy all of your sentry guns and droids (3 of each if fully upgraded), and then run to the safe spot. The map is small, so it can be any place, where you are not under fire, just keep running and let your droids and turrets make the dirty work for you.
Don't worry, you can keep grinding your 'Pimp My Arsenal' achievement after the final fight, as the game continues after the end credits (which are very funny btw). Moreover, the choice of available missions after killing the Subject 88 is great, and will let you to get only those you really need for the mission achievements.