After you meet the chief of Coralcola and the guard lets you pass, you enter the cave beneath Coralcola.
The Cave under Coralcola
From the dungeon entrance, go north to the next room. Kill the three slug monsters, known as Jellies. Go north through the door that opens.
Kill the six Jellies in this room, then go north through the door that opens.
Kill the Jelly to the right of you, then jump onto the tile on the right side. From there, jump to the tile north of that, then jump to the tile on the right. Kill the Jelly to the right, then jump to the right and go south. Kill the Jelly on the tile, then jump onto that tile to make a switch appear. Jump onto that switch to open the door to the north. You can optionally kill the rat monster, known as a Rattus, then go north through the door.
Go east, killing Rattuses on the way if they get in your way. At the east side of the room, go north and jump across the tiles in the water. When you reach the door, jump onto the tile to the south. This reveals a switch to the left. Jump onto the switch to open the door, then go through.
Kill the three Rattus and two Jellies to open the door. Go through.
Jump onto one of the tiles just north of where you entered the room, and jump north again to the next set of tiles that are side-by-side. A switch will be revealed, but it just opens a door to a dead end. The tile next to the one that you jumped on also reveals a switch, but it also just opens a door to a dead end. (These dead ends both have a skull-shaped floor and a bunch of bats, known as Noctos. You have to kill all of the Noctos to unlock the door.)
In the room with a lot of tiles, don't go through either of the two doors, but jump west until you are in front of the western door. Then jump onto the tile to the north, then jump east, and jump east again. Then you can jump north until you are on the strip of ground along the north wall. From there, jump onto the northwest tile. This reveals a switch to the east. Jump east and jump onto the switch to reveal a hidden tunnel in the north wall. Go through.
To open the treasure chest in this room, jump onto the upper-right tile in the southern half of the room. This reveals a switch. Jump onto it to open the treasure chest. Take the torches. You can switch to the torches by pressing SELECT, or by pressing START and using the directional pad. Just keep in mind that you only have a limited number of torches. You can keep using the star/yoyo for now.
In the northern half of the room where you got the torches, jump onto the bottom-right of the four northern tiles. This reveals a switch. Jump onto it to open the door, and go through.
Kill the northeastern Rattus to open the door, and go through.
Kill the Jelly, then go east and kill the snake, known as a Looper. Beware that it will charge toward you when it sees you. Go north and kill the Looper that comes from the east side of the room. Go north and jump across the tiles until you are on the west side of the room. Go south and pick up the torches that you revealed. Jump onto the middle of the five tiles, then jump north, and you will reveal another switch. Jump onto that switch, then go east, kill the Looper if you didn't already, and go east through the tunnel that was revealed.
Go to the south or north part of the room and jump onto one of the tiles on the south or north part of the island. Then take the Medicine. If you use it, it restores five hearts. To use it, press START to pause the game, then press down or up on the directional pad to display Magic Items. Move the cursor onto the Medicine if it's not there already, then press A to use the Medicine.
Then you can jump onto the southeast tile on the island to reveal a switch. Jump west onto the grassy part of the island, then jump north until you can jump onto the switch. It reveals a tunnel to the north. Go through.
Take the Medicine from this island, but beware. Jumping on the tiles around the island will reveal a switch, and the switch will open a tunnel to the north, but don't go through! The room north of the second medicine room is a dead end full of water, and you will drown!
Instead, go south until you can go west through the tunnel. Kill the Looper that attacks, then go west. When the Looper charges at you, jump or go east so you can avoid it. Then jump across the tiles until the north door opens. The treasure chest is empty, so just go north through the door that opened.
Kill the Noctos and Loopers in this room, then go north and you will face the C-Serpent.