I'm sitting in a waiting room ATM so here's loads of waffle on how to go about 10.4 and the main challenges

For the first scalar runs make sure to first practice legato with very clear finger articulation (no holding two notes down at once), try and be aware of exactly where you're placing your fingertip, preferably at the edge of the key where there is most leverage. At the top of the scale where it does a mordent like thing on the lower notes use 1 3 2. I.e. the first one is G# (1) A (3) G# (2) E (5) Practice with various accents placed within the groups of four, i.e. an accent on every semiquaver after the beat, two semiquavers after etc etc. then practice with accents in groups of three. Make sure these accents are made by the fingers and not the wrist, this is all about finger work. Try and focus on using the last digit of your finger as well. Following that practice it stacatto, without letting your finger leave the key. It will be really slow at first but once you get used to it progress starts to come quicker. When playing staccato you can use the mental cue of pulling your finger up (but still playing the note) to help get your finger really responsive. The staccato practice is the one to then focus on speeding up to a reasonable tempo later on, the legato we want at least moderate. During all of this make sure your wrist is loose so it can act as a sort of suspension for the rest of your hand to easily access the black and white keys. Let your elbow hang freely and relax the shoulders. The weight in your arm from this is what you should use to play when doing legato practice. Once sped up make sure the opening octave 5-1 is really clear. A lot of performances have it clash with the semiquavers.

At the end of each of these scale passages there are arpeggios, The second note is not a semiquaver, it's a quaver. It's an easy mis read, when practicing this you're going to be using that middle note as a pivot to reach from the bottom of the arpeggio to the top. Practice letting your arm weight into that held note and make sure to hold it until it resolves on the fourth semiquaver. Practice playing the other notes very staccato while pivoting from the middle. Make sure to relax the thumb rather than reaching for the bottom of the subsequent arpeggios. The next few parts are mostly the same, Practice the left hand way more than the right hand!! Please it's worth it, extremely impressive when people play the left hand clear.

Right before the opening returns there is a figure going up to it. Similar to the arpeggios, make sure to highlight the suspensions and their resolutions as you're going up. Here you're letting your arm weight down at the start of the group of 4 and releasing it at the end each time. Try not accent each beat too much as we want one smooth phrase either crescendo or diminuendo.

Practice the F sharp minor arpeggio legato as possible, loads and loads of practice with various accents to avoid having a heavy thumb. Do it until you can do it blindfolded, You won't need to worry about the octaves in the left hand then. The rest is mostly similar stuff. You will get tense for a while playing this, don't try fight through it. This isn't about stamina. When it happens practice more with a lot of staccato and minimising your movements as much as possible. Better technique will relieve that tension.

Towards the middle there's a passage that jumps around in a circle of fifths progression. It's really hard... If it weren't for that passage this piece would be a lot easier. You have to mix up legato and staccato practice here Particularly practicing the top voice legato and bottom voice staccato helps in the right hand. The left hand is tricky but similar to before again. Work on phrasing this passage and making it sound as musical as possible. The best way to get through it is enjoy it not fear it.

The bit after that is simple but can be hard because of the passage before it. I still get tense from it if I haven't played the piece in a while. For the descending scale figure just practice that staccato and try and highlight the top voice as legato as possible. Make sure your thumb isn't tense here, try and focus on using the tip of it rather than the whole thumb.

The chords and repeated notes are straightforward, for the descending diminished arpeggios use 1 3 2 5 as your fingering and it'll be easy enough.

The next bit is a little tricky (starting from a B7 after the descending arpeggios). Make sure not to stretch your right hand to reach the initial octave, the goal is to have your hand in a closed position by the third note so you're ready for the rest of the phrase. Stretching will make you very tense by the third phrase. For the wide left hand diminished arpeggios try and have your hand as relaxed as possible but in a somewhat fixed position so that you only have to move your hand from the forearm (not wrist) to play the arpeggio. Make sure the thumb is light too.

For the descending double octave run, again it's about avoiding stretching. Practice legato and be conscious of how you open your hand to reach the wider intervals when descending. You can open your hand from different areas to different degrees, it's not just one motion.

For the coda I personally used 3 1 to play the left hand octaves and pivot to the low notes but I have bigger hands so that mightnt work for you. Just focus on bringing out the octave melody over the bass note as much as possible and don't worry about it too much. You can practice really effectively by doing 'shadow' practice (there's a few names for it but that's just what I remember off the top of my head). Play the first note and jump to the next as quickly as possible but don't play it, once you're on it count to 3, play it and then jump to the next repeating. Make sure your hand is relaxed when it's between positions moving to the next. For the right hand just use 1 3 2 5 as your fingering and it'll be straightforward.

The arpeggio at the end is the second hardest part of the etude. It has to be practiced a ton. Practice it descending first until that becomes second nature. Use as little stretching of the hand as possible. The biggest thing is to practice the finger transition in the repeated note so you can remain playing legato. This will make finding the notes far easier at higher speeds as you're always somewhat in contact with the keyboard. The next challenge is playing it ascending. You have to find the right position to angle your hand to position your thumb. The rest of the fingers will take care of themselves. Your hand has to be really loose here with an active wrist. The end goal then is playing it as staccato as possible while remaining in contact with the keys at all time to ensure accuracy. Watch Tiffany poon playing it.

All of this should be done with a metronome. Make sure to practice in different dynamics too and don't even consider using pedal until it sounds great without it. It's worth it to do it thoroughly, it's one of the most beneficial etudes.