Once inside the palace, go up one and bomb out the west wall.  Now go west through that door and again bomb the west wall.  Before going through that door, be sure you got a full life gauge and the Red Medicine bottle plus several bombs.

If do, go through that door and wipe out all the blue Darknuts with the sword.  When that is accomplished, go through the passageway.  On the other side of the passage, go south into a room and bomb that room's east wall for a hidden door.  Go through that door.  If you got at least 100 rupies, get the bombs.  You should be able to have 12 bombs now.

Now return to the room with the hidden passage way.  Go through the door on the west wall.  You must wipe out a second group of blue Darknuts in order to open that passageway.  If you do, open the passageway and get the Whistle.

Now go back through the other passageway and return where you wiped out the first set of Darknuts.  Now go east until you find the room with the three Dodongos.  Go east into a room.  From that point on, you will be going North until you find a door that is going west.

When you start going west, look out for Pols Voice and Like Likes -- they're everywhere.  The third room that you'll enter in that direction is Digdogger.  Go get your whistle and blow it.  When the Digdogger shrivels up, a single mini-Digdogger appears.  Go for your boomerang to stop it, then hit it with the sword two times.

When that happens, the container heart appears.  Take that and go through the north door that had just been opened for the Triforce fragment.