This is the hardest achievement to earn once the waves increase in difficulty. It doesn't matter if your team mates you perks but you cannot use any. You can play the game as you would normally but you must not buy any of these perks:
Quick Revive Soda (Quick Revive)
Speed Cola (Sleight of Hand)
Double Tap Root Beer (Double Tap)
You can try the following methods to get through the waves or try the other two methods which follow below. These may not work for you, but you may be able to adapt them to your play style and get through the waves at your own pace.
Perk-A-Holic 3 Player Guide
Perk Addict made easy Guide