Normally, the shield is obtained mid-way through level 7, Eagle's Tower, however if you've completed the trading sequence prior to visiting the tower and have the Boomerang in tow, you'll be able to snag the shield right away.
Upon entering the tower, immediately head down the hallway to the right and continue until you come across a room with a locked door. Dispatch the pair of Like Like and a key should drop from the ceiling. Use it to unlock the door and proceed upstairs. In the room above you'll find a chest surrounded by orange pegs, making it accessible from where you entered, however, the Boomerang can be thrown at an angle over the pegs to flip the switch, allowing you to grab the dungeon's main treasure.