Recommended Item: Pegasus Boots
Total Rupees: 300
The Dungeon Bros' dialogue will actually change depending on which strategy you use to complete the dungeon. Completing the dungeon as intended, with the Pegasus Boots, will yield the traditional "nice dash" text. If any other strategy is used, you will instead receive the "Impressive technique" message, complimenting you for solving the dungeon in a non-standard way.
It is the act of physically dashing over the gates with the Pegasus Boots that changes the message from one to the other. The "Impressive technique" message is the default, but it will be changed to the "nice dash" message if ever Link dashes over even a single gate on his way up to the chest. Dashing by itself does not preclude you from getting the "Impressive technique" message, so long as you never cross a gate. If you do dash over a gate but still want to receive the "Impressive technique" message, you can reset the dungeon by leaving and re-entering, so long as you haven't yet opened the chest.
The Dungeon Bros' follow-up text changes as well, and this change remains even if you leave the dungeon and return. It even remains if you save and quit. The game actually records how you beat the dungeon as a flag, and persists that flag on your save file.