(Additionally, #4 is the only clue that neither begins nor ends on the yellow line. "Homeric" isn't strictly accurate, but it could be the solution if 'Hydra' is #1 and 'Ogres' is #2 The clue's thematic analogs could be: the Hydra, the Titans of Tartarus (Prometheus & Atlas if the theme turns out to be mythos), Herc's rookie status, the Erymanthian Boar, Nimean Lion, Phil, and Zeus's lightning bolts.
There's no orientation point (a pre-solved first clue, for example, already printed in) and no means of cross-checking your answers, which makes having such vaguely defined parameters the biggest obstacle here (does 'Green' have to mean "new", as per its relation with the theme? Or could it also mean ill, verdant, dyed Hydra does fit for #1 but that does't establish a pattern). My only issue with this interpretation is that we only meet ONE satyr in the cartoon.I don't want to assume linguistic imprecision, but we can't rule out the possibility. It *was* specified there'd be a pop-culture element, so this tracks. Canonically, Heracles trains to be a hero under Chiron the centaur, but the cartoon portrays him as a portly satyr named 'Phil'. OP included 'satyrs' instead of 'centaurs', so the relationship is pro-o-obably "Disney's Hercules", and not the actual Greek hero.