The Trap Door, also known as TrapDoor or Assult Door, is an enemy in the Final Fantasy IV series.
The only way they can be fought is by pressing the action button on a locked door at the Sealed Cave and can never be fought as a random encounter. They are far stronger than the other enemies in the area.
Trap Door will lock on to one of the characters with Target, then cast Ninth Dimension on the next turn, instantly killing the targeted character. An easy way to defeat the Trap Doors is to wait for it to cast Target, then have Rosa cast Reflect on the targeted character. When the Trap Door casts Ninth Dimension, it will kill itself instead. This works in all versions of the game.
Rydia can usually kill Trap Doors with one cast of Bio depending on the Moon Phase. This is the fastest way to kill Trap Doors which is important when repeatedly going through Rydia's Challenge Dungeon.
If Rydia has not learned Bio yet, simply have her cast Stop on the Trap Door as soon as she can. This will easily prevent the Trap Door from casting Ninth Dimension which can instantly kill someone and will also prevent the Trap Door from summoning a monster when it is low on HP.