H.E.A.V.E.N. mode:
To unlock Heaven-A, -B, and -C, defeat Gryphus (Stage 8 Boss), then go through the door behind you when you re-enter Primordium (Level 0).
Highest floor in H.E.A.V.E.N. mode:
To unlock the highest floor in H.E.A.V.E.N. mode, beat all 99 levels.