You can use a power washer. Just need to have the spray in a fairly wide fan and avoid the temptation to go really close trying to get stubborn spots off. Coin car wash is one option to get the worst of the gunk off. It's been done several times to my trailer without problems.
Important to rinse before scrubbing, you don't want to rub dirt with you cleaning brush or rag, it leaves scratches (think sand paper).
I used a scrub brush with a handle and trisodium phosphate (tsp) available at big box home improvement or paint
stores. Good general cleaner that rinses well and leaves no residue.
Barkeepers Friend (BKF) a powdered bleach that is mildly abrasive (really mild) applied with a wet rag or scrub brush. Think super mild Comet.
Green pot scrubbing pads (3M) be aware that if you bear really hard on them in a small area of fiberglass they can leave scratches, there is a less abrasive pad, I think it is white.
Green scub pad and BKF worked well on aluminum to clean as prep for polishing with Semi-Chrome (online or auto parts store, may have to order) or Nev R Dull. Be aware that aluminum polish creates a black "haze" that will get on your fiberglass if you don't use something like masking tape to protect the fiberglass. Key thing some aluminum polishes leave a protective film, some don't.
Auto Detail scrub brushes available at auto or big box retailers. Think big, stiff tooth brush for nooks and crannies.
Mine looked pretty much like yours when I got it, started with power wash rinse, followed by scrub brush and BKF, followed by rag, scrub brush or scrubbing pad with BKF on stubborn spots. Followed by wash with TSP.
Polished aluminum, rinsed and applied RedMax Pro floor wax there is a whole thread on that subject with pros and cons of these types of wax on fiberglass campers.
I like cleaning, it makes a huge, highly visible improvement :-) Don't forget to post "After" pictures.
Results (yes those are tree reflections on back left edge of roof):