You can do this. You could put an air handler up there and the compressor outside. If you go with high-velocity ducts, the outlets are small. An alternative that works if the layout is fairly open is a split system. This has a unit with (usually) multiple compressors mounted outside, and indivdual fans and evaporators inside. Some can handle up to three zones. The units do take up some wall space, but are quiet since they only contain the evaporator and an air circulator fan. Often, they are mounted high on the wall and are controlled via a remote that also acts as a thermostat.
Putting the compressor in the attic isn't probably a great idea, it's already hot enough and it gets inefficient dumping the waste heat up there. It could be mounted on the roof, but servicing is tough and the roof may not be designed for the weight along with a snow load.