This is the last(8th) quest for the College of Winterhold.
This quest is actually quite short and easy. Its just one "boss" fight and shouldn't take you anymore than 5 mins. To be honest i didn't even kill him the magical anomalies did. Its that easy!
All you have to do is use the Staff of Magnus on the Eye of Magnus. This will make it 'break up' and Arcano will become vulnerable. This is your chance to do some damage to him, or leave him to the anomalies and Tolfdir. Once the Eye has reformed, Ancano will go back and start doing his thing again. Just Rinse and Repeat till hes dead.
The prerequisite quest for this is the staff of magnus. Where you have to travel through the Labyrinthian. Here you will encounter Trolls, Wisps, Skeletons and Wizards.
There are 2 "Boss" fights in this level. The first being a Skeleton Dragon surrounded by about 8 Skeleton warriors, mages and archers. Save before using the lever to open a gate (which drops again after about 5 seconds)
If you have trouble with this boss (he had me for his dinner), reload your save from before you entered through the gate. Equip your unrelenting force shout and shout through the gate. This should bring the skeletons towards you. They can't attack you through the gate and you cant attack them with normal spells and weapons. You can however keep using your unrelenting force shout on them. This may take 5 mins to wipe them out because of the cooldown time. The skeleton mages didn't seem to be affected by this for me. So what i did for them was open the gate walk up to it and cast spells at them. As long as you dont enter the room the dragon skeleton will not rise. This allows you to focus on the dragon skeleton, making this fight alot easier. The dragon uses Ice attacks so counter him with fire(if your using magic). Try and keep away from his front because he can pick you up in his mouth and insta' kill you.
The Second boss fight is at the end of the dungeon. Morokei is, i beleive, a dragon priest and so he is fairly strong. Use your bow to take out the Wizard Thralls first. Then I recomend using ranged weapons or spells to take Morokei on. Run up the stairs where the Wizard Thrall was and he shouldn't follow you, or attack you. From here use your bow to take him out. When hes dead search his body for the Staff of Magnus and a awesome mask.
Enjoy the quest and i hope i helped :D