The "large amount of money" in the achievement description is 300 shells. It is quite possible to get this by the 5th chamber, but depending on your luck, you may get it earlier, or not at all.
A tip for getting this would be to check all the shops you come across, and sometimes there will be a grating near the back. You will see an interesting character under the grate, and you can drop unwanted items there (by pressing down on the d-pad) and he/she (it?) will give you shells in exchange.
Another easy way to obtain this will be after you've killed the convict's past. You unlock the possibility of finding a "briefcase of cash," in your runs, which will grant you 250 shells and 3 hegemony credits. Then you only need 50 shells for the achievement.