I get thirty minutes a day and I mostly play the bits I can already play, how should a short session be structured?

Thirty minutes is plenty. The problem is not the length, it is that you are performing rather than practising, and playing from the top is the clearest symptom.

A structure that works in half an hour, with the times as a guide rather than a rule:

Five minutes, warm up with purpose. Not a vague noodle: something technical that relates to what you are working on. Scales or an exercise in the key of the piece.

Fifteen minutes, the hard bits only. This is the session. Take the two places you stumble, isolate them to a few bars, and work them properly - see the next answer for how. You are not allowed to play the parts that already work.

Five minutes, join them up. Play from a few bars before each difficult spot through to a few bars after. This is what actually integrates the work, and it is skipped almost universally.

Five minutes, play something for pleasure. Anything. This matters, it is why you sit down tomorrow.

The rule that makes the whole thing work: never start from the beginning. If you want to run the piece, run it at the end of the week, once, and treat it as a performance rather than as practice.

How to work the hard bits, because fifteen minutes of repeating a difficult passage at full speed is not much better than playing from the top.

Make the chunk smaller than feels reasonable. Two bars. Sometimes one. If you cannot play it correctly three times in a row, it is still too big.

Slow enough to be perfect. Not slow enough to be nearly right, slow enough that it is genuinely correct every time, including fingering and dynamics. If you are making the mistake at this speed, halve it again.

Hands separately first if they disagree, then together at the speed the harder hand can manage.

Only speed up after three correct repetitions, and by a small step. If it breaks, go back down. This is the whole method and it feels absurdly slow for about a week.

Practise the transition in and out, not only the passage. Most stumbles happen at the joins, and a passage practised in isolation often falls apart when approached from the bar before.

What you are actually doing is refusing to practise mistakes. Playing a passage at full speed with an error in it is rehearsing the error, which is why it has survived a year and why it is always in the same two places.

Two things that make a short session much more productive.

Decide what you are doing before you sit down. Thirty seconds, written on a sticky note on the music stand: bars 21 to 24 hands together at 60, and the left hand jump in bar 40. Without that, the first ten minutes go on deciding, which usually resolves into playing from the top because it is the default.

At the end, write the next session's note. Then tomorrow starts immediately.

Record yourself once a week. Phone on the piano, play the section, listen back. Playing and listening are genuinely different tasks and you cannot do both well at once - there are things in your playing you will only hear from the recording. It is uncomfortable and it is the fastest feedback available without a teacher.

And the honest note about a year of the first two pages: that is what practising from the top produces, mathematically. The opening gets played every day and the end gets played almost never. Practise the piece backwards sometimes, start from the last section and work towards the beginning across the week. It feels strange and it fixes the imbalance immediately.