How can I install ceramic tile over vinyl tile?
Is the glue residue hard and rough or soft and gummy? If it's hard, a 6" floor scraper should break it loose, maybe with a heat gun or some boiling water to loosen it a bit. If it's soft and gummy, the scraper should get it by itself, or you can try some acetone or mineral spirits to dissolve it (make sure you ventilate the area well, and take frequent breaks).

Either way, tiling directly over a vinyl floor is not going to be ideal. The thinset will not key well to the smooth vinyl (and trying to rough it up will basically just get you to the point where you might as well scrape it all off anyway). Vinyl floor should NOT be considered a "floating underlayment", either, as a few posts I've seen have indicated. It's too thin, and actually MORE likely to result in cracking as tiles break loose and try to shift.

You really need to get that stuff off. It will not be an easy job, and if he's not paying you for the time he should be.