At higher grades you must be able to discuss with the examiner musical features such as texture, form, style, and period of a piece of music. My own web pages to help with these parts of the test at Grade 5+ and at GCSE are available here!
It is important to memorise horizontal lines of music rather than each chord as it comes.
Break the piece into its structural sections eg Exposition, Development, Coda etc
Work at the level of a short phrase - two to four bars at a time will be enough to work on.
Learn one part / hand at a time. If necessary, play the first beat of each bar only as you start to put the parts together.
Establish the rhythm of the first section, breaking the beats up if necessary
Establish the basic harmonic shape (eg tonic - dominant - tonic)
Memorise the simplest shapes first. For example the bass line if it moves stepwise, or a repeated pattern in the melody.
Where textures are rich it works if you can to think of voices and memorise them separately a few bars at a time.
Spot as many repeats or sequences as you can.
Say notes out loud as you play them when memorising (some people find this helpful when sight reading too).
Talk to yourself about other features too (eg. "This is a repeat of the right hand part, but up one octave" or "This is the opening phrase transposed to F major").
Play very slowly so you have time to think and plan. Try not to rely on muscle memory.
When you have played the section you are working on from memory a few times to your satisfaction, leave it alone until a bit later the same day.
The following day, check you can still play that section from memory before going on to the next section.
Don't feel obliged to start from the beginning of a piece or carry on from where you left off. Sometimes it is good to work on the ending or an interlude with a different mood instead.
If you are going to play this in a concert or an exam from memory, check how secure your memory is by trying the following:
Can you sit with the score in front of you and 'hear' it and play it in your imagination?
Can you play through the section in your imagination even without the music on front of you?