A few ideas come to mind here …
First of all, I’d suggest cleaning-up some of the geometry at the base of the object (the “left side” of this shot). The geometry on the right is clean; the geometry on the left is not. It would literally be the work of just a few minutes to clean the left side up.
Then, you need to add some explicit seams and maybe some extra faces. For instance, that right-side half would be very easy to deal with if you put an edge right smack-dab up the middle of the face that’s closest to us, including the middle of that curved section leading up to it. (More or less “right where the middle-of-face markers are running right now.”) Select those edges and subdivide them once… presto. Then make that a seam.
Another good spot for a seam would be to “slice away” that complicated bottom portion.
Different areas of the model will need to be selected, then unwrapped individually using a projection most appropriate to it. The seam-placement is chosen to make that as clean as possible.