I think, since this is a story with a solid midpoint, I'd suggest using the "but" method. At the moment, it reads like any other story, suggesting that his disappearance is the inciting incident. I get the impression this isn't the case so using a well-placed "but", you could make it feel as though there's a MPR (midpoint reversal).
I'm not sure you need "adventurous" or "lone". You're using a singular "hunter" so it suggests he's alone, and this is reinforced by the rest. "Adventurous"... well, he's off hunting a mysterious creature so that's fairly obvious. Instead, consider a characteristic that gives us his motivation, or his arc. For example "stubborn" or "headstrong".
Don't bother with "bunyip" it means nothing. Also, I think just saying "beast" is fine. If you said something like "mysterious" or "mythical" then you get the hint that it's elusive but also a big unknown.
Final thing, when it gets to the second part, pick a protagonist. Have a central character who's leading this search. Don't make it a group because in order to understand why this hunter MUST be found, it's easier to do it from one emotional perspective. Maybe a brother, then you can play nicely with the similarities and differences between them. It also means you can give us a little more character in the second half of the story. Oh... is their goal not to find him btw? Do they know he's died? The audience does, sure, but if he's out on his own do they actually believe he might still be alive?
I hope this helps.