Once you've strengthened an Astral to max level, "EVILve" it. EVILving your Astrals will increase their max level, and they will sometimes gain new skills. You can EVILve each Astral twice.
Once Astrals reach a certain level, you can reset them. Astrals will lose the skills they have acquired, and will return to LV1 of their original form, but their base stats will greatly increase. By repeating this, you will be able to strengthen your favorite Astrals to their fullest.