I know of two ways. Build a large deck, or build a retaining wall.

My grandfather was a stone mason, and we lived on a hill. He built a solid retaining wall out of stone already in our yard to hold in his very big lawn. The lawn was flat and that wall was much higher than it appears yours would need to be.

Suzi

Why do you want to level the lawn? What do you want to be able to do there that the current setup doesn't allow?

It sounds like a lot of work/money for not a lot of benefit.

I know all we need to do is tilt our computers, but why use a photo that misleads? Why not submit a picture where the camera is held level so we can get an idea of what the slope "feels" like? Via the picture is the only way we can grasp the space.

Wouldn't a level yard fill with water when it rains?

The photo is helpful to see the general idea of what you seek to do. But a photo does not provide any of the horizontal or vertical distances needed to suggest a successful design.

The vertical drop from the grade at the house down to the wood line or property line (whichever becomes the project limit) will remain the same as before regrading. Any part of the yard made more level will concentrate the vertical drop in a smaller area making it more steep.

Having the vertical drop in a retaining wall has the advantage of not taking up any of the horizontal space of your yard and is not subject to erosion. Cost is the downside.

Where space is not at a premium, achieving the vertical drop with a sloped grade can be cheaper. Slopes are more trouble to maintain and can be subject to erosion.

Regardless of the method used, there is a savings if soil can be taken from one area to fill another area in an equal amount. That way you neither have to buy fill or have extra soil trucked away. Looking at your photo, I doubt you would want to lower the grade near the house to balance the fill needed near the tree line. A better plan might be to take soil from the high area at the rear of you photo to make the needed fill.

Unless you are willing to make detailed measurements needed to produce a scaled base map of your property, that's all the help I can offer.