For Hazama: Just spam j.CCCCC, it "staggers" the boss quickly during normal phase and easily reveals the core during lazer-charge. Also does really nice damage to core itself. This was one of the easiest characters for me and I don't think I used anything else during the fight, except for sentries maybe
For Rachel: j.A > j.A > j.B > j.C without double jumps a couple of times should be enough to reveal the core, I saved OD Lily's to core phase.