I used to do a lot of that work. It is not easy to explain everything, but the basics is waterblast it to remove as much as possible and test the strength of the surface. You can then apply Hydrochloric acid, scrub with a bristle brush until it looks like it has been removed and water blast again. This might leave some whitish residue which most often fades away after a couple of months. You should apply the acid while it is wet from water blasting.
If this is concrete from other slabs laid you are going to need very strong acid say 4 water to 1 muriatic (hydrochloric) dilution and quick scrubbing followed by water blasting. It will be very difficult, but you will succeed.
If it is mortar from building of brickwork it will be much easier.
We used to vary the water force by using 3,000psi, keeping the tip moving back and forth sideways and bringing the tip closer from about 6 inches to one quarter inch and quickly moving it out again. That way you can see what force is required to move it and you can see when it is doing damage. Do not leave the water jet close to the pebbles for any lenghth of time, keep it moving in and out.
You need to know that the acid will react on the concrete stain and start to break it up. As it hits the stain it neutralises quickly so you have to blast away the softened surface then do it again. Keep applying acid, brush quickly, water blast the surface until it gets down to an acceptable appearance. Do not use the acid long term to soak it, do not use the water blast jet alone to remove it.
I would also caution you about the splash of acid onto other things, about immediately rinsing down things close by and also rinsing off the water acid each time. The pool may be the best place to put it all (ha, ha, try and stop it), but you would know better than me.
