If you want a code compliant, long-term reliable shower, you cannot just tile the floor. Code requires a waterproof pan that runs a minimum of 2" above the top of the curb...you do not have one. Waterproofing just the floor does nothing to improve or abide by that requirement. Keep in mind that concrete is NOT waterproof, but is not damaged by being wet. If some of those walls are wooden stud walls, they're probably toast if the shower was used much at all. Throw in the fact that that appears (?) to be a simple floor drain and not a clamping drain, whatever you do, if you want it to meet code, would require cracking some concrete to replace the drain with a suitable one.
Other than that, if you just want tile there, it's still messy, as you'd want to raise the drain cover to match the height of the tile. FWIW, you cannot use a paint remover, and to get a reliable bond, you'd probably have to mechanically grind off the top layer of both what's left of the paint, and down far enough to remove any soap scum or body oils, hair conditioner, etc. that may have penetrated into the top layer of the concrete. You won't be able to do that easily all the way up to the walls, it's messy, and time consuming. The reason for that is that any contaminants there will act as a bond breaker and the thinset mortar won't bond well long-term. The waterproof layer must also be sloped a MINIMUM of 1/4"/foot from the walls to the drain.
IOW, if you want this right, it's really a tear-out and replace not a patch with tile.
Check out
www.johnbridge.com for help in building a shower that will work and last.
