For this you need to have found a combined total of 10,000 gold coins throughout the game. You do NOT need to hold 10,000 at the same time.

You are allow to SPEND the coins. No need to keep 10,000 coins unspent for this. It just counts the total you picked up.

You should reach 10,000 coins naturally without any grind while going for all Chalices and Lost Souls. The Lost Souls require you to replay the story a second time, a lot of gold will come naturally during that step. Gold coins come from chests, barrels, smashing sewered hands/rats, and from money pickups on the ground. Pick up money whenever you see it. If you got all other trophies and are still missing this, the quickest way to farm coins is by replaying "The Crystal Caves". Unfortunately there's no way to track how many coins you picked up in total if you spend them. For that reason, it does help to not spend them, but that will limit gameplay a bit, up to you. You can also write down how many you spent to keep track.