Very easy to obtain, as the achievement states use no abilities, this include also abilities that are always active (like the life regen bonus of the medic, the increased crit rate of the hunterss and so on).
Just upgrade the weapons, be sure to get the chances to ban options to remove as many non weapon upgrades as possible to reduce the chance of errors.
This achievement is very much compatible with the other one requiring to complete a run with just two survivors as it will reduce the requirements for the ban perk (4 down from 6).