Related thread: https://forums.gearboxsoftware.com/t/golden-path-new-mini-event/4548707/24
I just started a new TVHM playthrough at level 65 mayhem 11.
For beating the first mission I received the cloning hunter seeker.
Please post more in here as you discover the rest.
My understanding of that event is: every story mission with gear reward (no customization item), will provide random world drop legendary for that type of reward.
Edit: it seems to be the same item each time. I got a hunter seeker again when beating chapter 1. Below you can see my concern if it wasn’t.
UGH. A random world drop isn’t as appealing. I can get that anywhere (5 minutes in the slaughtershaft, for example). I guess it needs more testing by the players.
If I could play a specific main story mission and get a guaranteed Lyuda, for example, that would be very nice for an event. Whereas, fighting through the other slaughter arena and surviving to the end to get a chance or two at Lyudas, is risky. I’ll try beating the first mission again on another character and see what I get.
Not if you are at Level 5 or so. It is aimed at new players, after all, me thinks.
I might run thru that way too. Does sound fun.
Playing TVHM on M11 I got a (both anointed M10 level) Hornet for “The Family Jewel” when I turned in the quest to Tannis and a Carrier for “Going Rogue” turning in the quest to Tannis.
I believe they are random world drops upon completion of the main quest line (about 20 ish quests), so about 20 ish random world legendaries if this is correct. Not efficient or worth it for farming them at endgame, but if you’re questing anyway because you want to, or if you’re going through at earlier levels, it might be a fun twist.
“Cold as the Grave” gave me a speedloadin’ hellwalker.
Random world drop? Thanks for nothing. I think I’d almost rather get kicked in the junk instead.
Stream team members noted a few are dedicated to specific items buuuuut…
The event is specifically for people leveling up new characters to give them an edge gear wise, to expedite completion of the story to head into Arm’s Race sooner.
Ideally, it’s for new characters, or ones you finished the story with but have all those extra levels to get if you skipped sidequests and DLC (something I have been doing so I can play then with mayhem active on new characters).
I run NVHM and then immediately run TVHM sans any sidequests or xp farming, so for anyone playing that way to level up, this definitely is a welcome perk of they are playing on lower mayhem levels or no mayhem.
Chapter 4 gave me a nemesis. And it gave the split screen profile a nemesis too.
I’ll try beating the first mission using a different character and see what I get on chap 1.
I am pretty certain it’s a specific item linked to each mission. Hunter seeker for chapter 1 seems consistent.
I got grave artifact for killing Pain and Terror
Whooopppeeee hunter seeker. Bring in the dick kicks.
Chapter 5 Sanctuary mission : legendary shield
It was either back ham or transformer. I accidentally marked the new flag as read.
One of the missions supposedly gives you a Lyuda. That’s worth it.
I think chapter 6 gave me a legendary class mod. In this case deadeye for FLAK. I’ll try to be better about marking all inventory items so I know.
Chapter 7 impending storm rewarded
Handsome jackhammer.
Chapter 8 rewarded
Hellshock!!! I have some already but more are always welcome!
Hammerlocked 
Lair of the Harpy = Quasar
Beneath the meridian
Cloud kill
But that’s standard if you talk to Ava. I didn’t try skipping the talk to Ava objective. Wonder what would happen there? Get it anyhow?
I think atlas at last gave me skins. In general if I don’t write it for a mission it was a skin or cosmetic.