You've got the right idea; brute force work. I haven't done too many tile jobs, but enough to see that there seems to be a specific tool that works best for THAT tile job. For example, I was removing 8x8" ceramic recently from a countertop and believe it or not, I found that a wide HATCHET worked beautifully for that particular job. I just held the hatchet (maybe 4" wide) at the base of the tile and struck the back of the hatchet with a hammer and it "mostly" just popped up beautifully. Some of it shattered and cracked, but really it was a matter of finding the right tool and hitting it the right amount. (By the time it's all up, you've gotten pretty good at it
Now in another installation, you may find that a 4" is too wide; perhaps hitting a prybar (maybe 2" wide) might work better.
This worked for me, but maybe a more experienced tiler will respond with an even better idea...
And oh yes, wear safety goggles and be sure to cover the job with something to protect against flying shards!
Hammers work great but then there is still mortar on the concrete that has to come up. I would suggest an air chisel. You can rent one really anywhere, and they work great on getting up the old tiles ( even if you want to save the tile floor)