You know those plastic scouring pads with yellow sponge on one side and green plastic scouring material on the other? Get a big one of those and use the scouring side first pass, then squeegee. Then just use your standard mop once you have greasy stuff wiped off for a final pass.
I did an end of tenancy on a student flat and it worked well on the bathroom window and kitchen window insides with mould and grease.