I’m all for doing stuff myself but recently am more of the attitude of working out the cost of buying kit + a day off work vs. the cost of a professional (doing it in half the time).
That said, an SDS* + chisel should only be about £120 and it shouldn’t be massively difficult to do once the first tile is up. It’s just when the professional then says “ooh - that'll need sorting before I start tiling” and he charges you another day anyway!
* this is the one I bought - Bosch GBH2000
I’m likely to go through the same process in a few months so let us know how you get on.
Also, is tiling-over-tile not an option?