That soil looks wet, compacted, acidic, and poor nutrients. Do a soil test, amend soils, and then consider drainage options. While tillage is normally considered bad, in soil like that it may be a good thing. Just regrading and re-sloping the ground contour, or a tile line, or subsoiling with a big chisel plow and a 200 hp tractor, or a drainage ditch, would be some methods of getting the soil drier.
In wet bottomland fields farmers often ridge their dirt into 30" rows over winter before planting fall cover crops, to avoid tight wet soils in the spring.