AI Limit has a total of 18 spells to collect for the Bookworm trophy & achievement. Spells are obtained by picking them up in the environment, defeating some enemies or bosses, and trading Adaptive Fragments or some boss Nuclei to Millaire. Obtaining all spells requires playing into NG+, as two sets of spells from Millaire are traded with the same boss Nucleus, so you need to defeat the bosses (Persephone and Eunomia) again in NG+ to receive a second to trade for the other.
DO NOT SELL ANY NUCLEI until you know you have all items required to trade for them, as you can’t get them back after selling and would need to obtain them again in another playthrough. You CAN equip Nuclei in your accessory slot until you want to trade them, as this doesn’t consume them.
Obtaining all spells is required for the trophy/achievement 
Bookworm (obtain all spells).
For trading Nuclei you can encounter Millaire in a couple locations early in the story which are optional for her side quest, but she will then move to the Temporary Campsite and stay there for the rest of the game, so you can return to her there at any time.
Spells
Below are listed in the order they are listed in the in-game Spells menu, not in the order that they can be obtained.
Spell #1: Railgun
Obtained automatically at the start of the game after defeating the Sewer Cleaner boss.
Spell #2: Flame Jet
Branch: Outer-Wall Ruins – Slums > Temporary Campsite
Obtained by defeating flamethrower Sewer Cleaner enemy along main path.
Spell #3: Missile Barrage
Branch: Sunken City Overground – Rooftop Street > Lounge
Along the main path you encounter a group of red Fisherman enemies on the broken bridge section. Defeat them all (or more specifically the jetpack enemy) to receive the spell.
Spell #4: EX- Railgun
Branch: Outer-Wall Ruins – Ancient Machine Works > Assembly Hall
While progressing you enter a room with a large robot that shoots lasers at you as you move around the room. In the room there are 4 silver and red pipe sections you need to destroy, after which the robot is destroyed and you receive the spell. There is one path each on the left and right side paths when going up to the next level, one at the back of the room directly behind the robot where you go to progress, and the final on up the ladder beside the robot and on the upper catwalk.
Spell #5: Ethereal Orb
Purchase from Millaire for Elite Necro’s Fusion Nucleus + 6000 Crystals.
Spell #6: Terra Inferno
Branch: Twilight Hill – Withered Forest > Deadwoods
From the Branch take the left path and continue along the left past the poison lake to where there are two Necro enemies with large arms. By the wall you can pick up this Spell. Path left leads to next Branch (green circle).
Spell #7: Scales Blast
Double check which spell you need in second playthrough as the game doesn’t prevent you from buying multiple of the same one.
Purchase from Millaire for Persephone’s Nucleus + 8000 Crystals.
Spell #8: Ethereal Beam
Double check which spell you need in second playthrough as the game doesn’t prevent you from buying multiple of the same one.
Purchase from Millaire for Persephone’s Nucleus + 10,000 Crystals.
Spell #9: Minimum Pain
Branch: Twilight Hill – Spirit Depths > Depths Bottom
Obtained automatically after defeating Persephone, the Stygian Queen of Woe boss.
Spell #10: Lightning Bolt
Branch: Sunken City Overground – Flooded Street > High Street
Go up the stairs from the Branch and pick this up from the ledge near the Pilgrims.
Spell #11: Lightning Hammer
Double check which spell you need in second playthrough as the game doesn’t prevent you from buying multiple of the same one.
Purchase from Millaire for Divine Vessel’s Nucleus + 7000 Crystals.
Spell #12: Lightning Cluster
Double check which spell you need in second playthrough as the game doesn’t prevent you from buying multiple of the same one.
Purchase from Millaire for Divine Vessel’s Nucleus + 7000 Crystals.
Spell #13: Spears of Punishment
Branch: Twilight Hill – Spirit Depths > Dormant Array
Before being able to reach this spot you need to have turned off the sentry eyes in the room. If you haven’t, go to Watch Tower Branch and then proceed past the room where the Panic Reaper and Cleansing Knight minibosses were and need to drop down the red platforms. The one that is sticking out farther has an invisible section that allows you to walk to the middle of the area. Ride the elevator up and interact with the button to disable the eyes.
You can then go back to Dormant Array Branch and take the path to the right where there are a number of Church enemies. At the end is a room with a white box that contains this spell.
Spell #14: Lightning Tornado
Purchase from Millaire for Clergy’s Nucleus + 12,000 Crystals.
Spell #15: Ignition
Purchase from Millaire for 10 Adaptive Fragments + 2000 Crystals.
Spell #16: Electrification
Purchase from Millaire for 10 Adaptive Fragment + 2000 Crystals.
Spell #17: Partial Reconstruction
Branch: Sewer Town – Southwest > Maintenance Access
To obtain this spell you must first obtain the Reservoir Key, which you can do by destroying the large robot at the end of the tunnel. Attack its hand closer to the right side tunnel in between it slamming the ground. Once it is out of the way carefully walk to the end of the platform on the right to pick up this key.
Now out of the room full of boxes below the Mud Ball maker NPC, follow the hallway to the door with the red light above it, open using the Reservoir Key. Continue through here until you take the ladder down into the area where the big robot was and pick this up off the ground by the floating enemy.
Spell #18: Trailblazer’s Oath
Purchase from Millaire for 15 Adaptive Fragments + 5000 Crystals.
For all other collectible types check out the AI Limit Collectible Guide.
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