If you already have the whip by the time you are in the Lanayru Mining Facility, you can use it to whip the lever in the first room to unlock the door. Simply run in the sand, target the lever and whip it. This skips the only requirement for the hook beetle in the dungeon.
Using Reverse BiTMagic, it is possible to enter the Gust Bellows room from the back door, making it quicker to obtain the Gust Bellows.
The corresponding Skyloft flag is set by Fi's Ruby Tablet text in the Goddess Statue. This is most easily triggered by entering the Goddess Statue with a file that has placed the Ruby Tablet, but not the Amber Tablet. The RBM can be performed by starting the file and clearing Fi's second textbox at the same time.
When you reach the first ladder in the southeastern room, pull out a bomb and start its fuse by dropping it. Use the Hook Beetle to ram the bomb into the ladder high enough to blow up the crate. This saves having to use the bomb on the pillar.
Once you reach the switch that opens the gates around the timeshift stone, stand on the front right corner of the switch and face the stone. Pull out the slingshot and aim slightly above the column on the roof that is seen above the timeshift stone. If done properly, you should hit the timeshift stone with the slingshot, instead of having to use the Beetle.
An alternate way to blow up the crate is to set the bomb down, pick it up again, and set the throw trajectory so that the highest point hits the ladder. Throw on the third fast flash (seventh flash overall), and the bomb should blow up the crate.
After obtaining the Small Key, save at the statue in the main room and activate BiT (Bombs are fastest, but the nearby Yellow Chu is also available). Now BiTWarp using the Upper Academy statue. Link should appear on the other side of the gate, and can hit the switch to open the gate, proceeding to get the Gust Bellows.
While this BiTWarp used to be done after the Gust Bellows, doing it before is slightly faster, as you are lower on health entering the dungeon (ideally on 2 hearts) than you would be after the Gust Bellows deathwarp (6 hearts).
The gate next to the second statue that leads to the main area of the hub room normally requires the Gust Bellows to open from the opposite side of the statue. However, this gate can be opened using Reverse BiTMagic.
The corresponding flag on Skyloft is the end of Fledge's first conversation in the Knight Academy, next to the barrels. This conversation can be accessed by entering the Knight Academy with a file saved before visiting Zelda at the very start of the game, including a Corrupt File. Perform the RBM by starting your file and clearing Fledge's final textbox at the same time.
It is possible to use the minecart in front of the Boss Door to ride across the gap to the right. This skips escorting the previous minecart through the Beamos gauntlet. There are two methods for doing so, but the one used in runs uses a bomb to trigger the minecart. See Unused Strategies for the Beetle Method.
After pulling the lever to call the minecart, place a bomb on the side of the cart opposite the Boss Door. You can use the bricks on the floor as a reference; the bomb needs to be 4-5 bricks away from the cart. Then quickly aim for the corner of the cart closest to the left Boss Door, and do a front hop jumpslash onto the cart. If you're quick, you have two tries to do this before the bomb explodes.
If done correctly, the bomb will hit the timeshift stone but not Link. If it hits Link, you placed the bomb too close to the cart. This is the faster of the two methods.
With good movement, it is possible to throw a bomb at the timeshift stone in the northeastern room and make it past the conveyor belts before the timeshift stone activates, preventing having to wait for them.
If you don't make it, you'll be carried to the lower level during the cutscene, wasting time, so you should either stop before the conveyors or make it all the way past.
While hitting the three switches to open the gate to the Ancient Circuit, it is possible to skip lowering the statues by using a bomb and the Hook Beetle to hit the switches through the statue. You must hit the left or right side of the statue base for this to work; the center is too thick and the explosion will not reach the switch behind the statue.
It's possible to do this hitting either the top or bottom of the statues, but the bottom is about 3 seconds faster overall due to faster Beetle flying.
Moldarach's claws and eye are based on number of hits, not damage. Thus, spin attacks and Skyward Strikes will not do extra damage. It takes 5 hits to destroy Moldarach's left claw (right as you're facing it), 7 hits to destroy its right claw, and 4 hits to destroy its center eye.
It's possible to get three hits in on a stunned claw at once by the following method:
If you do two slashes right away, you will be unable to get in a third.
By modifying the above, it is possible to use the slingshot to stunlock one of Moldarach's claws, thereby defeating it in one long combo.
This stunlock can also be done with the Clawshots during the second Moldarach fight in Sand Sea.
The most important part of Phase 1 is to back Moldarach up against a wall. This will allow Phase 2 to be completed before Moldarach burrows. Use either a shield bash or the slingshot to stun a claw, then use the above strategies to destroy it.
Note that once one claw is destroyed, Moldarach will sometimes attack with its tail, which wastes time as it is never vulnerable during that attack.
If you properly backed Moldarach into the wall during Phase 1, then you can defeat Moldarach before it burrows by chaining stabs right after its center eye opens. It takes 4 stabs to finish Moldarach; however, sometimes stabs will hit during invulnerability frames, so it may take 5 or even 6 stabs to actually kill it. Just keep spamming stabs until it dies.
If it escapes the stabs and burrows, just use the Gust Bellows as normal to unearth it and try to stab-lock it again.
It is possible to jumpslash over the spikes in the sand room before you remove the sand with the gust bellows, allowing you to go directly to the switch. Unfortunately, this is actually slower than running around the spikes normally, because the setup for the jumpslash is too slow.
Pull the lever to call the minecart over to the Boss Door. Go to the side of the minecart across from the left side of the Boss Door. Aim for the center of that side, and do a front hop plus jumpslash to get onto the mine cart. This may take several tries. Once you are perched on the minecart, use the Beetle to activate the timeshift stone. Be careful not to move as you cross the pit; the smallest movement can cause Link to slide off the cart.