Old asphalt floor up, what can i put down before tiling?

This is actually happening at my house (although in my case it was a wooden subfloor).

Take out as much as you can of the base. Starting from scratch seems to be the best idea. My contractor is using what I think it a bit like drywall for the base. I'd ask at Home Depot or the like (even if you don't end up buying materials from them). Wood could be an issue because moisture makes wood warp.

My contractor is also using levels to be absolutely sure (he's got 2 in my bathroom right now) he's got everything flat. You might also want to use more adhesive than usual; he's using a spreader with less space between the teeth (I don't know the technical names for these things) in order to make it easier to spread the dark gray stuff.

Hope this helps!