It's difficult to gauge the degree of slope by looking up or down (in line with) the slope, or looking across the yard in only one snippet. We need to look across and see the whole, wide view from house to lake. If you could return to approximately where picture number 3 was taken, adjust your position to be halfway between top and bottom, and then take a series of slightly overlapping photos looking across the slope, that capture from house to lake as the camera pivots (not changes locations), I think we could get a better idea of the degree of slope you're dealing with.

Do you have a septic system? Do you know if you have ledge rock? The part I circled looks like a mound. That where I though there might be rock.

I would decide how much flat yard I wanted and move the earth around to accomplish it. Hold back with a small retaining wall and provide steps. You can get clean fill but it is usually filled with rocks. You have to make sure the supplier has a good record.

You have an opportunity to add wild flowers and native bushes on either side of the way down to the lake. That area would not need mowing.

How much can you spend? Should it be formal or casual? Terracing would be one option.

Lakeside Terraced Backyard · More Info

Lakeside Terraced Backyard · More Info

This is less formal

Water's edge · More Info

Water's edge · More Info

Some thoughts on two projects:

One: What is the most practical path from the point of origin at the house to get to your dock -- the path you now use ? Would that path begin at the corner of the house closest to the yard toys -- either a straight or curved path -- until you get to the toys and then from the toys beyond them to the dock? That walk path is where you should begin to create dirt steps about 4'-6' wide by using railroad ties strategically placed across the path as temporary small retaining walls to create level or gently sloping "steps" between the rail road ties -- digging to throw dirt above or below the railroad ties as needed.

As you walk, you might take two or three steps on each dirt step you create. As you use the dirt steps you can see what steps work best and what steps need to be adjusted before you invest in blocks or stone for more permanent retaining walls for your grass covered dirt steps).

Two: you might consider putting a retaining wall all along the lower point of the yard where you usually cease to mow -- below the hill. Literally dig a deep ditch for a footing/foundation along that line above which you cannot safely mow. You could then put rebar in place and have concrete poured into the ditch (BEFORE before you remove the dirt from below the ditch/concrete wall so the sides of the ditch can serve as a form for your retaining wall) -- before you throw any that dirt from below the ditch to above it.

Once your poured concrete has set up, you can add a bock wall atop it, then begin to remove the dirt from below the concrete retaining wall to above the concrete retaining wall, adding other layers of concrete blocks to the wall as you are able to reach it from either above or below until you've achieved a reasonably level area both above and below the wall. You could then face the poured concrete with stone or brick if you choose..

DO make sure the bottom of the ditch you dig is lower that the ground level you want for the lower flatter area below the poured concrete retaining wall..

A ditch dug with a back hoe or other equipment will be wider that what you might dig by hand and take more concrete to fill but with the wider concrete wall you're pouring, you're building strength into your retaining wall.

Do post some after pics to show us what you've done.

Railroad tie (or landscaping post) dirt steps/path:

https://www.diynetwork.com/how-to/outdoors/structures/how-to-build-outdoor-wood-steps

https://homeguides.sfgate.com/landscape-timber-steps-54556.html

https://www.pinterest.com/pin/204280533078122075/

https://www.pinterest.com/pin/96897829454823731/