Bring in a dump truck load of chicken manure. Chicken manure is hot and will kill the grass if it's too fresh, so have it dumped in a pile in your driveway for 3-4 months unless you're really sure that it's had time to start to decompose/compost. You want to do this in the fall anyway, so starting now and letting it sit for the rest of the summer is the proper timeline.

Once weather starts to turn cool and your grass starts to go dormant, put on a good 3" layer of chicken manure all over your yard. At this point don't worry about trying to level out mounds, dips and bumps. Just get a good layer loose all over the yard. Don't compact it or try to work it in. Just let it sit over the winter and let the manure decompose/compost and the nutrients work its way into the soil.

In April, spread a thin layer of topsoil or topsoil mixed with sand on your yard and use a leveling rake to make everything level. Then roll it with a heavy weighted roller. As the weather turns warm next spring, the grass will work its way through the manure/soil/sand, and you'll have a perfectly level yard. If there are spots where you've got too much material on top of the grass, you can re-seed those areas.