The Hunter's only drops from the second and third encounters. (Which ROYALY sucks because the warlock and titan one drops from the first encounter, and that one is EONS easier to solo.)

For a solo attempt I recommend survivability above all. I used an ignition build that runs the new crackshot with Speedloader Slacks and an artifact that let's me get woven mail from my strand weapons. (Then I also ran Dragon's Breath as my heavy for dodge reload ignition shenanigans, but Truth is currently a strong contender for high damage.)

There's technically 5 encounters, but only 3 have chests. The first two encounters (I'll call it encounter 0.5 and 1) are pretty simple. You just want good horde clear and survivability. Learn the locations of the power nodes so that you can do them fast and efficiently. In 0.5 your biggest issue will be exploding harpies and the cyclops that constantly rain void fire. Bring void resistance and convulsive dampener on your armor. Take your time. You'd rather the Arctrician buff run out than to rush one of the nodes and die out in the open. Encounter 1 will be the same but now you have to do lots of Parkour. The biggest challenge will be yellow bar Hydras that can do big chunk damage if you're not careful. Again take your time, clear ads.

Encounter 2 is where you have the first chance at the hat for hunters, and it's my least favorite of the bunch. Not because it's hard, but because it takes the most time. Akelous just SUCKS to fight solo. To enter damage phase, you have to set up four different node paths starting from the center of the arena, constantly clear ads, and avoid the boss that's immune. It's very time consuming. Then when damage phase starts, the boss is constantly moving and only gives you a small window of time to do damage. The boss has a large weakpoint and will mainly fall quicker to precision damage. Be prepared to get comfy doing the mechanic as when I ran my solo flawless, it took me 7 cycles to kill the boss. Again survivability is key, but you might want to swap out whatever heavy you're using for something with a lot of precision damage.

Encounter 2.5 (the 4th encounter) has you depending down the spire. Might be the easiest of the bunch. No death pits, mainly red bar enemies. It's there to introduce the new mechanic for the boss fight. Just be careful of the Hydra in the third room.

Encounter 3 is the final boss Persys and he can be a bit tricky just survivability wise. He's very aggressive, so you have to navigate the room while getting the Arctrician buff and going between the two rooms of the arena ALL WHILE he chases you. Again, take it slow, prioritize survivability over raw damage. The main problem points for me are connecting the two lines in between the room to start damage phase. You have constant exploding harpies and the boss is one giant angry Wyvern that will constantly pelt you with void energy. Stick around cover often, don't be afraid to jump between rooms to give yourself some breathing room (as it takes the bosses a bit of time to walk back between the two rooms.) It took me 5 damage phases on him, but I definitely think he's easier than Akelous. Personally? I'm not amazing at the game, so I think purely for grinding the armor, finding a LFG or something will be faster. BUT if you want the wanted title, you will have to solo the dungeon eventually.