Note: The solution has been slightly rewritten since the March 19. patch, where Torbs health and Overload numbers have been changed. The achievement is significantly harder to get now.
This achievement has changed a few patches ago since the character was reworked (and then changed again). Right now the Overload ability gives you 100 armor instantly on the top of your base health (200 + 50 armor) for 5 seconds. You get increased damage, speed and firing speed this way as well. The armor is TEMPORARY, it will disappear. Since it is impossible to get this in one go the suggested method is overloading in a safe corner (near the enemy) and poke at them. If you lose the armor then back off and wait for the ability to regenerate. Best to do this near a health pack because unlike most buffing abilities this extra armor won't heal you. So if you for example have 100HP when you overload, you will still have that much when it expires. Ideally, if you poke with 250 and 100 armor you can't be one shot by anyone except if they get damage buffs so it is relatively safe to pick on solo snipers (from afar of course) who guarantee losing the full 100 every time.
Why is it harder: Before the latest patch where you got 150 armor from the ability you only had to survive 4 overloads (600 armor overall) with a lot of leeway. Now you must survive at least 5 if you lose everything every single time which is a huge risk.