The Eastern Palace is the first dungeon in The Legend of Zelda: A Link Between Worlds. It is rather easy in difficulty and has three floors.
The First Floor
When you enter the dungeon, there are three entrances to the next room, but they must be opened by a switch. The entrance on the right can be opened by stepping on a switch in a corner. This leads to a dead end with a few jars. The center entrance is blocked by a gap. On the other side is a switch that can be shot with an arrow. Hitting the switch with your arrows will cause a bridge to cover the gap and opening the entrance allowing you to proceed to the next room.
In the next room is another orb switch; this time, shooting it will open the left door, allowing access to a treasure chest with a red Rupee.
Heading into the next room are balls rolling in the center corridor. To help dodge the larger balls, you can stand one one of two alcoves nearby. When you reach the end of the center hall, turn left and enter the door.
In this room, the door will shut, and you will encounter three small enemies called Popos. They can be killed in one hit. After the three Popos are killed, four more will appear. On the top platform, a treasure chest will appear after killing the enemies. There are two exits to the next room, one under the platform the chest is at, and one in the southwest. Enter the southwest door.
The path in this room wraps around the perimeter. At the end, head to the door to the previous room. This leads to the upper platform with the chest that has the compass. The compass will locate all the locked doors and treasure chests in the dungeon. Jump down and head to the door underneath the platform. Stepping on the switch will make a treasure chest with another red Rupee to appear. Head back to the southwestern door in the previous room and step on the floor switch to open the closed door. Then head to the door you just opened.
Now back in the main room with the rolling balls, walk across the room and you'll find a locked door. Step on the switch on the narrow path nearby to open the door. One of the Armos statues will come to life, but it can easily be killed. Continue to the next room to the right.
This room has two orb switches and a moving platform. To shoot the switches, stand on the platform and shoot them when you are level with the switch. Head to the treasure chest in the corner to receive a small key.
Fairy Fountain
A secret fairy fountain can be accessed south of the room. When the moving platform is lowered, walk south into the secret fountain. There are three fairies in the room, and if you walk into one, they will heal you. You can also collect one with your net and store it in a bottle.
Going Up
With the small key in hand, return to the central room, and use the key to open a locked door at the top of the room. The door proceeds to the second floor.
Miniboss: Four Armos
Now on the second floor, there is a switch in the middle of the room. Step on it to activate four Armos. After defeating them will open two doors and open a portal to the beginning of the dungeon.
Finding the Big Key
There are two doors you can go to. The one one the left leads to a room with rolling balls. The one on the right has shooting turrets on the walls and is optional.
The Western Room
Step on the switch for stairs to appear, then run up them. Proceed to the southern half of the room while avoiding larger balls.
There are two switches you can step on. The first one near the center will cause the stairs to disappear, with a switch in place of the stairs. Stepping on this switch will cause a treasure chest with monster guts appear. The other switch is at the bottom left corner and will open the adjacent door.
The Eastern Room
From the room where the four Armos were fought, you can enter two rooms. The one on the right has turrets on the wall shooting arrows. They can either be avoided or blocked with your shield. This room has a treasure chest and four Popos. All four of them must be killed to make the chest with monster guts appear. There is also a switch on a ledge you can step on, leading to the next room.
In this larger room, there are two orb switches in the northeast corner. The northern one will cause a platform to vertically move, and the other switch will open a door to the right.
This room has two moving platforms, several wall turrets, and four orb switches in the center of the room. Shoot all four switches for a treasure chest with a small key and return to the previous room.
In the center of the room is the boss door, but we don't have the big key yet, and it's inaccessible. Stand next to the door, and shoot an arrow at the switch to enable another moving platform. Stand on the platform and open the locked door.
Stalfos and a Large Treasure Chest
This room has three Stalfos. They can be easily killed. After defeating them, open the large chest to get the big key. Climb up to the upper ledge and strike the orb switch.
The Final Switch
Return to the large room to find the final switch now vulnerable to your arrows. Shoot the switch for the floor to flip, allowing you to open the boss door.