Here's my take on the objectives:
1)Humbaba --an advanced era barbarian unit -- must be dead (Thanks Leif). He is a real monster just like in BOTM 41, but now lives in a fairly secluded place.
2)You own at least 2 Legendary culture cities.
3)You are EITHER the United Nations Secretary General OR the Apostolic Palace Resident.
4)You have learned Future Tech 1.
5)At least one AI opponent has been eliminated (conquered) by your team.
6)You own at least three Holy Shrines
7)You own at least three Corporate Headquarters
8)You have stolen EITHER Iron Working, OR Astronomy, OR Physics using espionage.
9)You fulfil the requirements for TWO victory conditions, at least one of which is NOT Conquest or Domination.
10) Blazing: You must submit a save covering at least your first 100 turns or victory or defeat - not later than 2 months after game start. **
1)One of the easiest. 2-3 nukes and he is down.
2)CRE trait, Lots of wonders, 3-7 cathedrals, hermitage, broadcast towers and the late game +50% culture wonders should all stack up nicely to ensure we get there in time. Sistine Chapel would be really helpful too. Something to keep in my is that Culture slider synergizes with Domination.
3)Really easy. Should probably abuse vassals for this one. Agree with Sengir that we shouldn't rely on Religious/UN victory. (but can take advantage of it if there's an opportunity)
4)Easy but will take a lot of time. We should check which techs we DON'T need to tech (probably crap like Advanced Flight). I think msot teams will abuse Corporations to get there faster. So should we.
5)Difficulty will rise with the number of turns that have passed but will once again fall down once we have acccess to nukes.
6)A little bit luck-dependant but hopefully we won't be forced to spawn a GP in the Modern Era

I hope the AI will do the hard work for us.
7)Sid' Sushi is easy if we beeline Economics, the Great Scientist corp (Standard Ethanol?) is even easier since we'll likely spawn a ton of Great Scientists. Mining Inc might be tough but I've already mentioned that running 4 engineers from Ironworks+Forge should help with that. For this reason we should try to get a really early Ironworks. Also, if we get an early Great Engineer as a lucky spawn we should definitely save him.
8)The best choice here would be Iron Working. But it's the toughest one as well. The other the are much easier but are much more appealing to research ourselves (Physics for the Great Scientist, Astro for early intercontinental trade routes, observatories and ability to colonize islands - if there are any).
9)You can already tell that I'm strongly in favour of Culture + Conquest/Domination.
10) We'll just have to play fast...