If it's 100% concrete slab as you say you can use a sledgehammer.

You won't damage the concrete floor, you arn't that strong.....
And little chip or divot you create can be repaire with SLC or concrete when you are done but I'll bet you won't have any....
After a few wacks with the sledge you should be able to slide a long crow bar under the tile and pry it all up...
in other words but your back into it.....
Oh and you MUST remove the vinyl... and if your shower tile was put on drywall, i'm betting it was a paint scraper should work.
If it was done properly a paint scraper and a hammer should work, just tap the back of the scaper to jam it under the tile....