If you want it to be precisely level, you can use a transit level or laser level to set clamped concrete forms similar to the ones in your second photo to the correct height. If you can't rent or buy a $2000 daytime visible laser level, get a cheaper indoor one and use it at dawn or dusk. Mine is a non rotary that cost me $40 second hand and would be fine at dawn or dusk. Your transit level will work too but is more time consuming and finicky. With a transit I'd probably drive spikes and set string lines to height on the outside edges of the wall, use the string lines to set the outside boards and a pair of torpedo levels to set the inside walls. As a 2 person job it isn't bad, but if you wanted to 1 person it, you may end up needing to drill inserts and screw the boards on instead of using clamps. When using a laser level or stringline in some cases it is helpful to mount the line or laser a known measurement high and then use a jig or measuring tape to copy the laser/line height down to what you're levelling. This prevents the edges of the pieces you put in from blocking or affecting the line/laser while you work.
Make sure you don't add additional concrete without applying concrete bonding primer first. Once your concrete is primed and your forms are on, you just pour to the top of the now level form and vibrate and trowel it level and smooth. Make sure you get a type of concrete meant for thin layers if you want to keep the existing top as the top. Alternatives would be to add the minimum thickness to the wall height at all points or chip the high points down first. It has to be bonded well enough it won't chip out when you drill or use powder shots to mount the walls on top. I see you've got some bolts sticking out there, and if you have foundation height problems you may have bolt height problems, so I would use a laser level and transit to check every bolt before you pour anything as it may turn out once everything is level you actually need to chip some of the high part out so the shortest bolts will be long enough.
No matter what you do you'll have some seam in your concrete, so it would be best if it was protected from moisture. The bolts make me think you might be dropping a quonsit on the slab that might not fully protect the top edge. If this is the case you could blueskin or at least epoxy seal the slab. The difficulty level of applying thin set layers that will endure moisture and frost cycles is much harder than always dry concrete.
One last thing, if you happen to decide to use a laser level that was used to lay this slab in the first place you had best check it for level before you use it. Place it in one place, mark the height on a bunch of things that are reasonably far away, then move the laser about 50 feet and make sure the height difference between your markings and the laser line is the same at all points. Some rotary lasers can be set on a tilt, but they should revert to level every time they're turned on.