I want to install a shower in an existing bathroom with a concrete floor. There is currently no drain in the floor for the showere. Is there any way to install a drain without breaking up the concrete floor?
No. You need to tie the drain into an existing line, which would be in and under the concrete. Providing you know the location of the main waste service for the bathroom, it really is not an incredibly difficult task (but will be time consuming and labor intensive) to cut and break out a concrete trench that runs from the shower drain location to intercept the main waste for the shower drain. If this is not a task that you are up to, hire a plumber, many professional companies have plenty of experience in what you ask.
But since this is a DIY forum, I would say do the following:
1) Frame out the rough opening for the shower
2) Remove the toilet (determine which way the waste runs)
3) Determine if the waste line is sufficient enough to tie into
4) Remove anything that will get in the way of the concrete saw
5) Chalk lines on the floor for trench to cut
6) Get a hose and a wet dry vac ready for the concrete saw
7) Go and rent concrete saw and jackhammer
8) Saw cut and jack hammer trench (careful not to puncture waste line)
9) Dig out dirt and rock around drain line (calculate for enough slope in drain line running to shower)
10) Make list of parts needed to run drain, go pick up parts
11) Install and get inspection, if permit was pulled
12) Backfill and compact dirt
13) Fill trench with concrete mix, trowel flat