How can I prepare this concrete floor for tile?
Putting tile over a painted surface can be risky. Sure looks like removing all that paint would be a chore and maybe hazardous (lead based paint if pre 1978).  We have put tile over such surfaces by roughing it a bit and putting a scratch coat of "floor patch and leveler"  over the entire surface. This is a good bonding agent on stable subfloors.

Another very good alternative is to use one of the new no-mortar interlocking tile products. These are tiles mounted on an interlocking plastic base that just snap together. They are very quick and easy to install. There are several different brands, tile material and backer types available. There is an article about these type of tiles, on Good Housekeeping.

Google "no mortar tile". Lots of articles on the subject