Fibonacci is the fibonacci sequence. Don't ask me whether it's supposed to be up or down though, I tried and eventually gave up cause my numbers were getting way too big. 
Pumpkin Eater is probably for cheating, "cheater, cheater, pumpkin eater"
I don't want to believe this because that's actually really stupid if so but Free Advertising is probably donating to the dev?
1/61 prob has smtg to do with chests opened much like fibonacci sequence. I couldn't tell you how to do it though, dev really needs more/better hints for these achievements imo.

How to get all mystery achievements is listed here: https://www.reddit.com/r/incremental_games/comments/1ivvwsc/lootbox_incremental_...

I think Fibonacci sequence should also be triggered if you buy least to most expensive too though, as that makes more intuitive sense, @tomlangamestudios .  I guessed that, but it didn't work, so I figured I was wrong.  

I had to do Ascending Collector twice for some reason. Didn't trigger the first time, but worked the second after I'd finished off some other stuff.