Kill the Cultists as soon as possible as they gain Strength each turn after the first. The Awakened One itself is straightforward to handle: match your defense to the specific attack and use the rest of your energy to deal damage. Once you lower it to 0 HP, it will become invulnerable until its next turn while removing debuffs like weakened and vulnerable. Use that turn to ramp up your defense and possibly play power cards that were saved, since The Awakened One will immediately use its Dark Echo attack. Surviving Phase 2 is mostly a matter of surviving Dark Echo -- especially the first one, which could catch unsuspecting characters off-guard. Save any exhaust cards that will help speed up this phase (e.g. Terror).
Watch out for Phase 1's Curiosity ability. Whenever you play a Power, the Awakened One will gain 1 Strength (2 in Ascension 19+). This is especially dangerous with the Soul Strike attack, which will use the Strength bonus four times. Even if you have a Power build, you might want to avoid using them during this phase. Curiosity goes away in Phase 2, so you might want to spam your Powers when the Awakened One enters its invulnerable state between the phases, or as soon as Phase 2 begins.
Use temporary Strength debuffs (like Piercing Wail) right before killing his first form. The debuff will permanently lower Strength in Phase 2, but not below 0.