This quest is probably the easiest and shortest quest of the College of Winterhold. All you have to do is kill 10 Ice Wraiths outside the College in Winterhold. I found that killing them is a pain because of their unpredictable movement and because they are pretty small.
The best way to deal with the Ice Wraiths would be by magic because you can spam that at their general location. If you don’t have magic and you are struggling I suggest you lower you difficulty, that is about all you can do.