The Legend of Zelda: Link’s Awakening certainly never makes it easy to get into the various dungeons in the game. The first one required a key and the second requires some help from BowWow to reach it, but now the third dungeon in the game, Key Cavern, follows a similar approach to the first with a key being required. First you must follow the previous guide on how to get the Slime Key and then you can move forward towards finding the actual entrance to Key Cavern.
After receiving the Slime Key, traverse back through the garden to Richard’s Villa until you get back outside of it. Now head to the left and up to eventually reach what looks like a key slot outside of a structure with bars in it. Now use the Slime Key to open this slot, but you will notice that your path is still blocked here to get to the entrance itself.
Instead, you have to make your way back around to Richard’s Villa and go east, north, and then west and you’ll find yourself next to a pool of water. At this point of the game, Link will drown if he jumps in, so instead you must use the platforms to get across using Roc’s Feather. Head towards the west and you’ll find the now open entrance to Key Cavern.