I too have stopped earning progress and its disappointing. My remaining ones are:
Make 25 Babies - 72% (18) - Have made a lot more than this. Vault is at 95, almost all of them are bred.
Level a dweller from 1 to 50 - 55% (27) - A couple of my initial dwellers are already 50, though levelled through exploration not working in the vault.
50 Room Rushes - 63% (32) - Have rushed a lot more than that.
50 Raider Attacks - 31% (16) - Have had a hell of a lot more than that, rarely see raiders now, just deathclaws.
Rooms upgraded to 3 - 61% (30) - All my rooms are lev3, which is more than 30.
Build one of each room - 13% (2) - When I get 5 more dwellers I'll be building my final room. Pretty sure I wouldnt have got this far with just 2 rooms.
20 Legendary Weapons - 10% (2) - The game tells me I've found 4 Legendary weapons so far.
100 Objectives - 59% (59) - Have done a lot more than this. Stat doesnt increase whether the reward is caps or boxes.
20 Legendary Outfits - 5% (1) - The game tells me I've got 2 Legendary outfits.
20 Legendary Dwellers - 5% (1) - This stat is accurate, only one Legendary dweller so far.
I've watched the stat, it doesn't increase when I make babies with different pairs, brand new dwellers (through the Radio room) or ones bred in the vault. Tried rushing lev3 rooms versus lev1 rooms, no stat increase. The last time I got a raider attack, the stat didn't increase, doesnt increase with deathclaws. Building extra rooms doesn't increase the "one of each", nor does building a single room, levelling it to 3, then building one next to it, levelling it to 3 (instead of merging them to start with, then upgrade).
I only have the one vault, haven't tried creating a second one to see if that helps... but the amount of hours I've spent in this one, I'm not looking forward to starting over.
I sure hope someone is looking into this. I like achievements especially for games like this to give me a feel for when I've done everything, but now I dont know why I bother loading it up. I'll just tap some resources, tap some stat increases and murder some deathclaws. Would like to be earning something again.