Gonna be kind of difficult to get an impact on there with the alternator installed. Take the alternator to a parts store like Advance. They usually have a very strong electric impact gun to swap pulleys for alternators they sell.
Another option is to take it to a tire shop. Those guns will zip that nut off like butter!
I got it off, I hit it with some wd-40 and let it sat for awhile. Took it off and brought it inside, since my impact is too loud outside. Pushed down hard on it and kept hitting the button. Took awhile, but it finally came off.