At the start of the battle, deal with the multiple spiders since they can still deal a great amount of damage to you, even with full health. AoE (area of effect) attacks works well against them since they can be easily killed. You can only damage the boss by attacking any of its two heads. The heads can alternately fire a straight but sweeping beam, corrosive acid balls or spider web balls that will restrict your movement. Fortunately, only one head can be active at a time. When you see it moving its head upward, anticipate that it will start firing its beam. Run towards it and attack the other head while its doing this attack. The boss also has a jump attack and will attempt to pin you down under its weight; you see it jump, evade at the last instant before it lands to make sure you evade safely. Be careful of the basic attacks using its limbs as well.
The acid projectiles are very easy to evade as well as the spider web balls. The latter doesn't deal that much damage but will prevent you from moving efficiently. During the battle, the boss will summon 3-4 more spiders to harrass you; deal with them as soon as you can. Ranged characters just need to keep circling; the boss isn't that fast to cloes the distance. Melee characters need to exploit the chance when the boss uses its beam attack; it's vulnerable for a few seconds, allowing you to land heavy, powerful strikes on its dormant head.
After defeating the boss, kill the remaining spiders and get the Great Soul near the edge of the arena. Follow the tunnel leading to the library and kill the undead facing the table. Loot the Brightstone Key, Fragrant Branch of Yore and Dark Quartz Ring +1 from it. There's a primal bonfire in the other room; however, you need to deal with the enemy first.
This is Vengarl's body. Vengarl is the decapitated head that you can talk to and buy items in the foggy forest area of the Shaded Woods. Defeat it to get Vengarl's Armor Set. This enemy is powerful and hits hard with bleeding effect but you can just keep circling around it and attack it from behind to deal heavy damage. Use the primal bonfire to return to Majula afterward.
Brightstone Key
You can use this key to unlock the door inside the building above the boss‘ lair. Take note that several spiders will attack you after opening the second door so deal with them first before opening the chest. Get a Black Knight Ultra Greatsword, Great Fireball and Fire Seed from the chest.