A pool, whether plastic, fiberglass, or concrete, whether it's a 6" kiddie wading pool or an Olympic lap pool with a diving board at one end, needs to be level. Completely level. This is just physics. If you don't want your water to be all down at one end, the pool needs to be on a level surface.
Visualize a plastic $5 Walmart kiddie wading pool set up on the side of a hill. Now, where's all the water? That's right--the downhill side of the pool is full, and the uphill side of the pool is empty, as in picture 1.
In order for the pool, and therefore the water, to be level, the pool would have to built out onto a supported, level surface, as in picture 2.
You can build a solid enough wooden deck to support a 6" deep $5 Walmart plastic wading pool.
You cannot, however, build a solid enough wooden deck to support even the smallest size of in-ground pool bigger than a kiddie wading pool. Water weighs 8.3 lbs per gallon, so a 16x32 in-ground pool, with 19,200 gallons, weighs 159,360 lbs or nearly 80 tons.
So this 80 tons of water has to be sitting on the ground.
So the ground has to be level.
So there's no way you're getting a pool built in your sloping backyard without involving fill dirt and a retaining wall, to build up the ground under the downhill side of the pool so that the pool is level.
So that's going to drive up the price considerably, as labor is always expensive--labor to bring in the dirt, labor to move it around, labor to build the wall to hold it in place.
Could we build our own retaining wall somehow?
Depends. How much experience have you had at building retaining walls to hold up 80 tons of water, and moreover one where the penalty for failure is so great. Your kids are swimming in the pool on the day the retaining wall, waterlogged by hurricane rains, undersized for the job, and incorrectly bedded on its footings, gives way, sending your children instantly downhill in a probably-not-fun water ride.
Not to mention sending 19,200 gallons of water into whatever is downhill from you, for a long, long way down, all the way down to the bottom. Roads? Neighbors' backyards? A daycare center? The possibilities for mind-numbing, viral media disaster are multitudinous.
If you want an in-ground pool on the side of a hill, it's going to be expensive. End of story. There is no way to cost-cut or DIY your way out of it. It's a specialized and very large and difficult engineering task and it calls for experts. Hire the best and pay them what they're worth.