Start a new game in New Game+ mode, on at least Action Girl difficulty. After starting the game, head to the elevator in the lower right corner of the lab, password is always the same - 1995. Remember to press escape three times in order to skip cutscenes which obviously saves time. Don't save the fairy bot, this will reduce the amount of dialogue you need to skip during the run. I recommend getting to the cutscene trigger placed in the room marked on the picture below, which will transport Alma to the Gear Village which is very close to the Mines entrance.



It is useful to kill both Shadow Creatures here with Greed chips equipped, which will help with buying Arcadia Keys from the shop when needed.

From the Gear Village, go left and down and enter the Mines using the entrance marked on your map with an icon. Upon entering the mines, follow this path:


Remember not to waste your keys. You will need many of them later.
On your way to the boss you will need to use your hook to pass the water, (Or use a well timed spinner attack jump) then you'll need to use your Fire Blade weapon to pass the green things blocking the way. (and to light up the four things in order for the boss arena to be accessible)
Remember to equip at least one Greed chip before finishing off the boss, as the bolts acquired from it will be used to buy a key that'll be needed in the Aquarium.
Use Spin Attack and Sword / Axe chips (stackable) to finish off each boss much quicker with spin attacks performed after a successful parry.

After being teleported out of the Mines, proceed upwards until you reach the Aquarium entrance.
Here you'll need to either move a block near a wall to the left and perform a series of wall jumps, or use a switch and the block it moves up, to get you high enough from where you can use your hook to get on top of the area. Here just destroy the block of rocks to the right using the Spinner and transport the orb to its destination to the left, in order to open the way into the Aquarium.



Now make sure to activate the Terminal and, if you haven't already, buy a key from the shop in Gear Village with the Merchant chip equipped for halved price. (if you can buy more than one, thats great but not needed for now)












Now activate and use the elevator down and follow this path:




Don't take any elevators, just go to the upper right locked gate and open it using a key.
Now use your double hookshot to pass the water and head to the lower left area. (Ignore elevators up until the boss)
There is a short puzzle along the way which I'm sure you can figure out in time (If not, remember that you can always make a copy of your save file before attempting something potentialy time-consuming, and if you lose a lot of time, just use that copy instead. I wasn't doing that and it cost me failed runs...)
Now proceed left past the elevator and here you have another puzzle which this time is optional but rewards a key. If you decide to do it instead of buying another key in the shop later, make use of the box picking up and placing down mechanic to make it easier for you to move the big statues around.
Proceed down and into the boss entrance room.
The order of switches you need to activate was the same for me every time: 1 3 2 6 4 5 (looking for the clues around the Aquarium is basically a reset sentence for your run.

Now just parry and spin attack the boss and if you are feeling badass you can equip greed chips which will help in the Museum as it has locked gates to use keys on.

After exiting the Aquarium (being teleported out) proceed to the left, then up and past the water into the Museum entrance. Now go left and look for a way past the locked gate. You'll need to fall down to the lower floor after turning the lights off (for platforms past the locked gate to appear) and come back up the elevator and go inside the room to the left past the locked gate. Now take the elevator up and look for a way up leading to the first of two switches needed to open the Boss room entrance located on the upper level in the middle.
You started with the left switch because that way leads to the second one anyway but the second one doesnt lead to the first. Don't be scared of using your keys here. There is a key along the way which requires you to put an orb into the hole to open a chest. Remember to buy keys in the shop in Gear Village when possible.

Now head back to the city streets and use your spinner spin attack to break through the Cathedral door. Take the elevator up and remember to open the chest containing a key here. It's in the left upper corner of the room just before exiting the Cathedral and into the Highway.






















Now proceed down, then right, then down again and now go left when possible until you see a locked gate. Use a key to open it and head up the vines to fight the boss.

This area always takes the most time, but if you don't remember the route while you do it, it will absolutely destroy your run. (speaking from experience)
Upon entering the Factory, make sure to open the gate (multiple switches required) blocking your way to the HAILEE robot.
You will need two keys here, so if you were unable to purchase enough in the shop, there is one key located in the upper right part. You need to disable the heat to get there, do it before touching HAILEE, then come back and proceed with HAILEE in this order:



Ignore the left side of the Factory completely.

Start from the middle of the Factory and go right towards the first HAILEE upgrade station.
Then come back to the middle and go towards the second upgrade station, here you need to solve a puzzle, remember that you can copy the save file and try again if you waste too much time on it.

The puzzle is basically:
- leave the HAILEE on the button to open the way to the right.
- fight the enemies there.
- go right and move the block from a button to the first button HAILEE is standing on.
- use HAILEE to push the big blocks in the upper part of the room and take the orb to the orb switch hole thingy.
- now move the block from the left side onto one of the buttons to the right.
- leave HAILEE on the second button.
- proceed to the right and past the upgrade station to unlock the way around which you can take while inside of HAILEE
- go around while inside of HAILEE and use the second upgrade station.

Now just destroy the gate blocking your way to the boss (middle part of the Factory) using missiles and repeat the usual Parry + Spin Attack ordeal on the boss.

After acquiring all of the shards, proceed to the Gear Village room Alma woke up in near the start, in order to forge your Meteor Axe.



Now only the Meteor Tower remains. Try dealing with enemies here quickly, but remember not to let your guard down as the Shadow Creatures can easily mess you up if you arent expecting them while rushing forward with your Spinner. (again, speaking from experience...)

Defeat the bosses here with your spin attack following a parry, the same for the Final Boss.
Ignore Raquel during the escape sequence if you need to save time.

And that's it! Hope this helps you during your attempts!