This is probably the most cost saving way to build your own whirlpool in your backyard. I've used an Intex 6ft above ground pool. The water is heated by a homemade heat exchanger on a BBQ grill. For the bubbles I used a Hailea 318 compressor and silicone tubes. Finally, I put a LED strip into the water to provide good vibes.

Supplies

Intex 6ft above ground pool
Hailea 318 compressor
4*6mm silicone tube
water proof USB LED strip
BBQ grill
1/2" threaded pipes and fittings

Step 1: Simple Heat Exchanger

I used 1/2" threaded pipes to create a simple heat exchanger: 2x 2', 4x 16", 5x connector,10x 90°elbow fitting
Connect the pipes as shown in the pictures. Use PFTE tape to prevent leaking.
The 2' pipes are on the outside to be connected to the filter pump.

Step 2: Setting Up the Pool

Ensure a level surface.
Set the pool up by filling air into the outer ring.

Step 3: Heating

Set the BBQ grill up next to the pool. Ensure sufficient distance.
Put the heat exchanger on the grill.
Connect the pump to the heat exchanger.
Connect the other pipe of the heat exchanger to the pool.
Turn on the pump. Make sure there is no leaking and water is circulating.
Fire up the grill. Put a metal lid/pot on top of the heat exchanger to increase efficiency.
Now you are heating the pool. You need a lot of energy and depending on the outside temperature this process can take a lot of time. To speed up, you can insulate the pool. At least, you should put a cover on the pool.

Step 4: Installing the Compressor

Put the compressor on a level surface.
I placed it near the grill to get warmer air. However, ensure sufficient distance so that the plastic parts do not melt.
Use the adapter to connect 4/6mm silicone tubes.
Put the ends of the tubes into the water. Use waterproof tape to stick the ends to the pool or use stones to weigh down.
For smaller bubbles you can use air stones.

Step 5: LED Strip

Use a waterproof USB LED strip.
Put the LED strip into the pool. Let the USB plug hang down on one side of the pool. It needs to stay dry
Power it with a USB powerbank.