Smarthinking pays about $12/hr for online tutoring work, done from home. For English, this implies reading essays of high school and college students and sending feedback according to highly standardized procedures that they train you in. ("Your essay should open with a thesis statement", etc.) They also do math, science and computer tutoring, but I know less about how they work. You choose how many hours a week you want to work and which hours (e.g., Monday 10-4) but they have to be the same each week (you are allowed skip some occasionally and just not get paid from them).

With 20 hrs/week it would only give about half of your targeted income, which might be too far. But if you think you'd find tutoring easy/fun and have problems finding customers out on your own (which would obviously pay more), you might give it or another company like it a try. (ETA: I think the company keeps for itself half of what the students pay, and certainly hiring a personal tutor must be more expensive than paying for anonymous, standardized online feedback. So getting a few students to hire you for personal lessons might give you enough to get close to your target. You would have to save for the summer though.)