You can start the fight sooner by throwing the boomerang or shooting an arrow (or bomb arrow) at the darknut.
Walking slash the darknut to make it defend, run around to its back, and slash six times. Repeat with six slashes for a total of 12 to end phase one. (You can also do five slashes on the first cycle and seven on the second cycle, but the point is that you have to time the sixth slash on at least one of the cycles.)
Bomb arrows can be used to peel off two layers of the darknut's armor per hit. This can save up to around six seconds over the slash method. There are two ways of doing this.
The first way is to shoot bomb arrows at the darknut's feet. Each shot can hit up to three times, so at least two shots are necessary. The number of hits per shot is inconsistent.
The second way is to shoot bomb arrows at the darknut's back. Each shot can hit up to two times, so at least three shots are necessary. The number of hits per shot is inconsistent. This method is a bit trickier than aiming at the darknut's feet.
The fastest way to clear the second phase is to hit the darknut with the ball and chain four times. There are two setups to do this:
The first way is to roll forward and turn slightly right before pulling out the ball and chain.
The second way is roughly the same, but it uses a jump attack out of the cutscene to get to the same spot. Note however, that this method cannot be used if bomb arrows were used for the first phase (Link will put the sword away instead of jump attacking).
If the above methods fail (for example, if the darknut blocks the ball and chain), the next best alternative is to walking slash the darknut, hit it with two sword slashes, and then pull out the ball and chain for three hits (throwing the ball and chain for the third hit often helps).
It is possible to skip the fight entirely with a jump strike moon boots bomb boost. 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 (he can, however, make it more difficult to target for the jump strike). Done quickly, this skip saves 29 seconds over fighting the darknut with ball & chain.
In general, perform this trick through the following steps:
Stand in the middle of the light tile shown in the video, pressed up against the wall, and put on the iron boots.
Line up the camera so that the large gold stripe is around the middle of the screen.
Target and use the bomb button to throw a bomb to your left.
Untarget and press B to pull out the sword, then begin to charge a jump strike.
When the bomb is just past the peak of its third fast flash (two-frame window), release the jump strike.
Pause on the frame below (one-frame window) and force unequip iron boots.
The bomb boost should make Link grab the top of the gate, and you can just climb over the gate and grab the dominion rod.
The frame in step 6 is shown below.
Bewildebeest has a more detailed video (on Gamecube) below.
Note that without Door of Time skip, the only real option for categories that finish Temple of Time is to use the big statue to leave the room.
Other darknuts can be defeated in the same way as this one, except that they have one fewer layer of armor for the first phase. For the second phase, the best way to defeat them is with two slashes followed by three ball and chain hits (as shown in the backup for phase two above). The main difference for the second phase is that it is possible to skip the walking slash by sidehopping through the sword throw at the end of the first phase and walking behind the darknut as it pulls out its smaller sword.