Also it's hard to tell from just the one screenshot, but possibly some portions of that shape can be created from a larger base object that then has some pieces carved away.

If that is possible then that kind of an approach tends to be the easiest starting point.

That process goes something like this - build an initial full simple shape, something like this (here using Loft between 2 curves):





Then draw in a curve in the side profile view something like this:



Now you can select the object and cut it by the side profile curve using the Construct > Boolean > Difference command. That will slice the object into 2 portions like this:



Then delete the piece that you don't want to keep:



Anyway, something along those lines may be an easier starting point. You'll still probably be creating other portions of the object by doing some sweeps though.

- Michael