From what I remember, each of those maps has a memory score along with a total power recommendation. If the total memory score of your four squads is equal to or higher than the map's score then you get better rewards upon clearing the map*. Your Knight's memory score is based on the rank of flower memory they use (6* memories are worth 5 points, 5* are 4, 4* are 3 and 3* are 2). The memory score requirement on the higher difficulty maps is 61 which can be met as long as you use at least as many 5* and 6* memories as you use 3* memories.

* For the standard flower memory maps you get low quality memory crystals if you beat the map but fail to meet the memory score requirement. If, however, you clear the map and meet the memory requirement then you get the same amount of low quality crystals along with some high quality crystals.