The easiest way is the level a bit further until the Evil City. Then unlock and max out the Gravekeeper Ghoul. The regular Ghoul from much earlier should be maxed out by now as well and both will give you a Stench Max of 60.
The base Stench you get is 10. 10 + 60 is already 70.
Next is to invest Sin on 'Inventory Creation: Cleaner', this will give another +10.
After that you can upgrade it another 30 levels through 'Inventory - Cleaner+', which gives another 30.
At this point you have reach the maximum Stench you can get through upgrades. The only other way to collect more is by investing in the Sin Inventory expansion 'Stench Max+'.
This gives a total of:
Base: 10
Allies: 40 + 20 = 60
Sin upgrades: 10 + 30 = 40
Stench Max+: 390
Total: 500
Having Smelly Satchels will help filling the max Stench because it regenerates. Once you hit 500 the achievement will unlock.