For jobs that small, I just use a 3 pound hammer and a large cold chisel. I can do it faster that way than going to the rental place, then returning the rental item and all the steps in between. Much less dust than with power tools. Helps keep the forearms looking good, too.

You can use a hammer drill and masonary bit to drill a series of holes in a line where you want it to break. This will give a fairly clean fracture line when you break out with a sledge hammer.

Drill stop holes in the corners with a masonary drill bit. Put a masonary blade on an old circular saw. You should get about a 3 inch depth with a 7 1/4 blade. Give the piece you want to remove a smack with a sledge. Drink beer for a job well done.

My contractor used this special blade (?) on his angle grinder to cut the borders, then used the chisel and mondo hammer method.

"any tips on doing this demolition beside renting a jackhammer?"

Do it by habd after drilling at least 4 holes inthe corners.
It actaully goes pretty fast if you use a hammer drill and drill ~1/2 inch holes every inch around the desired hole.
You can then score as deep as you can get with a circular blade down the line of hole and chisel the hole by hand.
Heavy jack hammering can easily result in cracks in places you do not want them.
A light touch is better.
A 2 or 3 pound drilling hammer is all you should need.

You should really look into getting a rotary hammer. They are quite slick to have. My wife rolled her eyes at the price of them but they go through concrete like a knife through butter. I have the Bosch Bulldog. You will not fear concrete with this tool. Hammer drills are worthless in my opinion, rotary hammer is what you need.

I would recommend renting a small rotary hammer and an SDS drill bit by the hour and just drill holes all the way around
where you want to work and drill a path of two lines down the middle so you can break the block in half with a sledge and have enough room to pry the concrete out. Wear eye and ear protection. Return rentals once you are done,
should only take a half hour to break up what you need. This wont be expensive and will be the easiest way.

But, if you want to do this the hard way, as suggested before use a circular saw with a masonry blade and cut the floor where you want to break it up. Caution: lots of dust, concrete dust is real bad stuff, wear good breathing protection and have a shop vac sucking dust and/or run a hose to where your working to make it a wet saw. Plug extension cord for circular saw into GFCI outlet if using wet saw method. Then use standard chisel and sledgehammer.