Rupees matter more in the remake: wallets grow to 1,000, the Great Fairies alone charge 1,175 over six visits, and in general things will be more expensive and enemies will drop less.
So here are a few easy ways to get Rupees.
Sell Bugs
Child & Adult era.
Sell bugs (and fish) at the items shop in Hyrule Castle Town. This is the most reliable farm in the game, and you can do it both as a child and as an adult. The best way to do this is to go to the patch of grass against the cliff just outside Kakariko Village. Then hit the grass and tons of bugs will crawl out. Fill all your empty bottles with bugs and then sell them at the items shop for 20 Rupees each. You can reset the grass by entering any other area and coming back (Kakariko is right next to the grass). Of course, the more bottles you have, the better. Here is our guide for All Empty Bottles.
The Pot Room
Child era.
As soon as you enter Hyrule Castle Town via the main gate, enter the house on your right to find it filled with pots. Break them all and you will get anywhere from 20 to 30 Rupees. The pots do respawn, but not immediately, so come back every now and then or just check whenever you are passing by.
Skull Kid
Adult era.
More than a farm this is an easy quick way to get a gold rupee (gold). As an adult head to Kokiri Forest and enter Lost Woods. In the first area, head left and a skull kid will attack you. Defeat him to get 200 rupees. He is quite agile so the best way to take him down is to close in on him with your shield up and then hit him a few times once you are close enough. If you take too long he will escape. You can try again by returning to Kokiri Forest. If you kill him it doesnt seem like he respawns.
100 Gold Skulltulas
This is by far the best way to "farm" Rupees, but at this rate it's not really a farm anymore, more like just "infinite Rupees". After you bring all 100 Skulltulas to the cursed rich man in the house in Kakariko, every time you talk to him he will give you a Gold Rupee (200). So you can literally talk to him, get 200 Rupees, leave the house until the door shuts, re-enter and ask for another 200 Rupees. You can repeat this as many times as you like.
