Here is the full list of all 86 Astral Ascent achievements.
Obtain 1000 Quartz in a run
Save all Yalees from the Kingdom
Defeat Aquarius
Defeat Cancer
Perfect 30 Fight Rooms
Unlock the Path of Destiny
Find the hidden nest in the Garden
Face The Master
Reach the Event Horizon
Defeat Libra
Defeat Lupus
Defeat Aries
Summon a Zodiac to support you
Defeat Capricorn
Success a Zodiac Challenge
Defeat Pisces
Defeat Sculptor
Equip an Astral Gambit
Defeat Virgo
Defeat Pegasus
Unlock Calie
Unlock Oloon
Captured 5 Astral Spirits
Unlock Papa Yalee
Unlock Barbecue
Defeat Hydra
Reach 1000 damage in one combo
Change a Spell affinity in The Sun Room
Reach the Crimson Highlands
Defeat Scorpio
Defeat Draco
Defeat Sagittarius
Equip 4 affinity gambits on a spell
Meet Chamaeleon
Unlock Octave
Start 30 escape attempts
Unlock Sire Bapy
Reach the Coral Archipelago
Defeat Leo
Defeat Monoceros
Reach the Red Barrens
Defeat Taurus
Unlock the Peddler
Equip an Astral Aura
Unlock Zim-Zim
Reach the Garden
Upgrade a spell to level 10
Reach level 12
Buy all items from an Itinerant Peddler
Obtain 5 Echoes in a run
Use 200 Stars in a run
Open 150 Key Chests
Equip a Zodiac Spell in The Moon Room
Your Zodiac sign helps you 3 times
Trigger 12 dialogues on Benches
8 stones of each type equipped simultaneously
Use your Signature Spell 500 times
Unlock all Zim-Zim abilities
Unlock all Auras from Barbecue
Unlock all spells from the Peddler
Unlock all Oloon colors
Collect all memory fragments for Papa Yalee
Complete 50% of Sire Bapy’s achievements
Defeat Gemini
Defeat Taurus at Destiny Level 6+
Defeat Virgo at Destiny Level 6+
Defeat Capricorn at Destiny Level 6+
Defeat Aries at Destiny Level 6+
Defeat Sagittarius at Destiny Level 6+
Defeat Leo at Destiny Level 6+
Defeat Pisces at Destiny Level 6+
Defeat Scorpio at Destiny Level 6+
Defeat Cancer at Destiny Level 6+
Defeat Libra at Destiny Level 6+
Defeat Aquarius at Destiny Level 6+
Defeat Gemini at Destiny Level 6+
Defeat The Master at Destiny Level 6+
Defeat 30 Star Guardians
Collect 100 Destiny Fragments
Activate all abilities of the Void Catalyst at once
Upgrade a spell to level 15
Success an escape at Destiny Level 15+
Unlock Ayla’s ending
Unlock Kiran’s ending
Unlock Octave’s ending
Unlock Calie’s ending