Practice the right hand by itself until you can play it perfectly 25%+ faster than ultimately required. Do the same for the left hand. Then put them together.
After playing a piece over and over and over with the sheet music, you will memorize some parts almost automatically. The rest you must consciously memorize.
I do so similar to memorizing a poem: play two measures looking at the music, then try to play them from memory, repeat until successful. Go forward one measure. Repeat.
Finally, in both the initial learning process and when perfecting the piece, spend an inordinately disproportionate amount of time on the sections that give you the most technical difficulties.
For sections of the music that repeat, don’t practice the repeat by replaying the repeated parts; otherwise you’ll overlearn that part compared to the rest. Conversely, overpractice the transitions between such sections and the rest of the piece; otherwise those transitions will never be learned as well as the rest of the piece.
One Idea 