Solving a 4-layer square-1 is just like solving a 2-layer square-1 twice.
First solve the top and bottom layers like a normal square-1, ignoring the middle layers.
Then solve the middle layers like a normal square-1, without turning the top/bottom layers at all. This is actually a bit easier since each side has two identical pieces, namely those with only one colour. The two-coloured pieces (the corners of the middle layers) are unique because if one seems to be flipped, it is really only in the wrong layer. Very similar to the edge pieces on a 4x4x4 cube in that respect.
If solving the middle layers has left the outer layers incorrect (the top layer right half and bottom layer right half need to be swapped), then alternate doing a half turn of the top layer with a half turn on the right hand side, until it is correct.
If the centres need correcting (the right half of the top centre is the wrong colour) then alternate doing a half turn of the top two layers with a half turn on the right hand side, until it is correct.