Throwing the Boomerang or shooting an arrow or bomb arrow immediately after skipping the cutscene after entering the room will start the fight faster than rolling up to the Darknut.
Running slash the Darknut to make it defend, run around to its back, and slash 5 times. Repeat with 7 slashes for a total of 12 to end Phase 1. Note that this is one more slash than the 11 it takes to remove the armor from all other darknuts in the game.
A bomb arrow shot at the floor behind the Darknut can knock off as many as 3 pieces of armor. However, it is difficult to consistently knock off armor with bomb arrows, especially if the Darknut blocks any bomb arrows with its shield.
Immediately after the mid-fight cutscene, roll directly forwards once, take about two steps, and press and hold the Ball & Chain button to twirl it. If done correctly, the Ball & Chain will hit the Darknut 4 times without being deflected, ending the fight.
It is possible to skip the fight entirely by performing a Jump Strike Moon Boots assisted by a bomb boost - see video below for setup. Link will grab the railing after the bomb boost if done correctly. Climb up and run along the railing towards the chest to hop off into the little enclosure. Run around the chest to open it. Either call upon the statue to break the railing or savewarp to escape. Note that because of the small step near the Dominion Rod chest, the Darknut will not be able to attack Link when he is in position to attempt this skip.