This is an interesting faction with something for all three specializations (Mage, Warrior, Finesse), though it is more oriented towards Sorcery because of the eventual rewards that you will receive. Nevertheless, there is something of interest for everyone here.
Kingdom of Amalur Scholia Arcana Faction Quests
You can begin this faction quest-line by going to the Scholia Arcana embassy in southern Ysa. Enter the embassy and speak with Docent Augra Tenet to initiate the first quest.
Trial by Fire
You now have access to the Delving Hall in Ysa, and that is where you will be heading. This is, as the quest’s name suggests, a trial, and you will be transported from one dungeon to another where you have to fight quite a few enemies. At the end of the trial you can talk to the sorceress and initiate your second quest.
The Ruin of Aodh
Go to Aodh in the middle of The Sidhe. There are quite a few Elemental Sprites in this dungeon, so make that as a mage you use the opposite elements to deal damage. At the end of the dungeon you will fight Nuala Ignis, a powerful mage. Once you finish her, return to Savant Engar in Ysa.
The Unquiet Bride
You have to rendezvous with a contact at the eastern corner of Tala-Rane. You’ll get ambushed by three bandits, and once you finish them off you can get your next task from the contact.
Head to Mel Aglir to meet with Patrick Morkan and speak to him. Go upstairs and loot the journal from the footlocker. Read the journal to proceed.
Now go to Tulan, and you will fight Patrick. Loot his body to find a key with which you can proceed further. Return to Mel Aglir, speak to Lerkara Fel, then go back to Savant Engar in Scholia Arcana.
Go to Emaire on the Forsaken Plain and speak to Anker Edmure. He will ask you to slay a Paragon Barghest, which you can find to the north.
Once you have killed it, loot its beating heart and take it back to Edmure. Now, in the western part of the Cradle of Summer is Shardfall, and you have to go there.
Go through the dungeon and you will eventually come across Cadoc Reen, a powerful mage who you will fight and kill. Return to Engar once done.
Lightning in a Bottle
You’re going to Skycrown, southwest of Rathir, in Acatha. Enter and be careful of the powerful enemies here and the glyph-like traps.
Once you have reached the peak, you will have to find where Engar’s body landed. It’s actually far to the south, in the southwest corner of Kandrian. Loot the corpse and return to Scholia Arcana.
A Crowded Mind
Head to the Archsage Quarters for your next objective. You will be trapped in the mind of the Archsage, and must free him from possession.
Make sure to dispel the first chest on the right for a note and key that will unlock the next chest. The chests in this area have keys in them that unlock other chests, so try not to leave any unopened if you want to read all the notes.
Before leaving, Caledus will give you a choice of reward. You can choose between ‘Fearless’ or ‘Disciplined’ Twist of Fate cards.
Place the keys in the statues to summon Ciara Sudanus. You will have to fight her with powerful summoning capabilities, alongside the ability to lay traps on the ground.
It is best to enter reckoning mode to do huge amounts of damage or attack her from range. Once done, you will get the Archsage’s Ring.