Floor Boards On Concrete

Drill, plug, screw.

For something like battens, which will be subjected to millions of load cycles over their lifetime (people walking on the boards), you need something between the screw metal and the concrete. If you don't have this, the holes will slowly widen, and the screws will come out.

Put some lead under them to deaden sound and put a layer of tar between the concrete and the lead and the lead and the 3 x 2.

Do you need to fasten the battens down? If properly packed and with furniture on top is it necessary?

While you are at it install some insulation between the battens if you can.

Hire a hilti gun or equivalent

your batten spacing needs to be 14" min

I was going to do this in my living room extension by taking up the screed and putting batons on the slab until I discovered that it was built without a dpc. I finished up digging out the concrete and putting joists in , hopefully you will be ok.

Kevin

Mm. Tile cement? (No) More Bollocks? Car body filler? Hilti gun and big nails? lay them down and in fill with screed?

Houses are not responsive to what you do or don't like doing: Only to what actually works.