You musty have the Havoc DLC pack. Load up Exo Zombies > Outbreak.
Simply get into a game with a friend or randoms and be exactly what the achievement is named, a cheapskate, buy NO WEAPONS, buy NO DOORS, do NOT go down or die and once your teammates open up the pathway to the Exo suit room (I suggest the path along the left so that you open HealthBoost/Juggernog on the way) simply activate the generator wired to it for free to power it on then walk up to the exo suit holder and press x to equip your exo.
Bing bang boop achievement unlocked!
Hope this helps
Happy Gaming!
-coreymawf