For these achievements, you need an "S" rank on every episode (including the secret episode) on hard and normal.
Ranking is based on three elements:
You need 3 "S"'s or 2 "S"'s and one "A" in these elements to get an overall "S."
The obliterator gauge will aid you for this one. Since you won't face much of a great opposition clear time isn't a worry, however battle points are. Just don't die, Use a lot of heavy attacks as there is no cooldown, and continue to fight even when the burst gauge is full to boost your rank, but not so long as to hinder your time rank.
Synchronic rate isn't too hard. Always be ready during cutscenes for those out-of-the-blue buttons, don't miss anything, and aim for mostly excellents. Do this and a "S" rank is yours.