Remaining Moments of Triumph, from easiest to hardest:
Challenge of the Elders - People run this every week, it's pretty fun and one of the best ways to get high level gear. Just get a partner or two who know how to juice that week's setup, run the challenge 3 times, and you're done.
Return to the Reef - I don't even remember checking this one off so it can't be that tough.
This Is Amazing - I'm a total PvP scrub and I was able to grind this out. It's just a matter of keeping going at it until you've checked off all the boxes.
A Blade Reborn - This is a grind-athon, and involves waiting a week in the middle of it, but aside from two tricky but not impossible boss fights, this is achievable. I got the grindy part in the middle of the quest done in ~4 hours.
The Sword Logic - You'll need a good group to run with, a LL ~320, a reliable exotic and an ability to keep your cool. This is the biggest PvE challenge the game has to throw at you, but it's doable if you're with someone who knows what to do.
Eris Morn's Revenge - Literally the hardest achievement in the game, it takes dozens of hours and tons of coordination with other players along the way. For hopeless Destiny addicts only.