The achievement text is a little misleading here. You must hold 3000g at one time, not just collect it. (As of v0.86b)
The best way to get this achievement is to play as the rogue. The rogue starts with the Lockpick, allowing a chance to open a door or chest without consuming a key. Use bombs to blast open clusters of blue vases as they can contain gold, keys and bombs. The rogue can also be used to pass through spikes (with the rogue bomb special ability) to collect chests in the room with 4 chests protected by spikes, should you see it.
Two artifacts that are also very useful on this run are Dynamite and Economicon. The former will allow you to get into more secret areas and destroy more blue vases whilst the latter doubles all money gained after picking it up.