How to soundproof floor from neighbors below?
There are two kinds of “sound control” problems: 1) airborne sounds, and 2) impact sounds.

Airborne sounds (talking, tv, etc.). When I first read your statement, I thought this was your problem because it occurs BELOW your unit. As soon as that noise travels in the air up to your apartment, it becomes “airborne sound”.

However, now I think it is an “impact sound” because you’re not complaining about other airborne sounds. Therefore, the clicking noise (from walking on the tile) must remain in the structure until the sound reaches your space.

Impact sound (closing doors, heels clicking on floor from walking, etc.).  Impact sound travels through building materials (floor joists, wallboard, etc.) much faster and much more efficiently.

In order to control impact sound, you need to isolate the surrounding material. Some of these problems are “built in” and cannot be resolved easily (or cheaply), which appears to be your situation.
For impact sounds we try to 1) stop floor joists and underlayment from extending under a party wall, 2) provide separate party walls between rooms, and 3) stop roof joists from crossing from room to room, 4) isolate the impact noise. Obviously it’s too late for those techniques.
The easiest remedy is to remove the tile and reinstall it over a sound deadening board to isolate the tile. However, I understand this is not an option. Therefore, I’d 1) check to see if the sound is just as loud in other parts of your apartment. If so it not, then maybe you could rearrange your environment (perhaps sleep in the living room). 2) If it’s just as loud in all parts of the apartment, then I’d build a sound isolation room within your existing bedroom. This may include adding music to mask the sound.