I don't have a food processor, can I just use a mixer?
Not to make the aioli, but you can use a whisk and a good amount of elbow grease! You have to create an emulsion and a mixer won't work for that. Here's a great video from our site about making aioli! it should help a lot : http://www.food52.com/blog...
Would a mixer not work if she has the whisk attachment for it? I would imagine the egg yolks and garlic would need to be minced or processed (in some way) first.
I think a blender would work too.
A blender maybe, but I really wouldn't mess around with the mixer - i just doubt it would work and you'll be left with a broken emulsion. I'd say just go for the whisk, bowl and elbow grease. More control, and super satisfying too!
Yes, I second the whisk and some good old fashioned elbow grease.