Here’s a basic error that everyone makes when they’re learning a new piece. Step one is fine – learn each hand’s part on its own. Even as early as step two though, it all starts to go wrong.
When you have the notes sorted out for each hand, it might be possible to play hands separately to near perfection – and that’s where the danger lies. You’ll try to do it with both hands together.
You’re going to get impatient, and when you try to play both parts together you’ll struggle through from start to finish, over and over again.
You’ll be frustrated that you can’t play through without wrong notes, hesitation, stumbles, slowing down or grinding to a halt at the tricky sections.
You’ll practise a tricky bit, then forge ahead to the end and when you get back to the tricky bit next time it all goes wrong again.
My recommended approach is to imagine that you are now learning a third part… one which uses the other two together, but requires different thinking. Play the first two bars, no further. Make a “loop”, playing bar 1, bar 2, bar 1, bar 2… without stopping, joining the end to the beginning. When you can go round three times without a mistake or hesitation, and ONLY then, learn bar three and do the same with bar 2 and bar 3. Advance one bar at a time until you reach the end of the piece.
Now do it in four bar sections, then in eight bar sections, then sixteen… until you’re doing the whole thing.
That’s how to achieve a fluent performance without the bar lines looking like trip wires, and it works because you’re learning to flow through the piece instead of focusing on errors.