How can I obtain the "Perfect as Tears" and "Like Stars in the Sky" achievements?
I think(not 100% sure) that you can get a lot of Flawless Square gems with help of one of your friends(or multiboxing).
A level 60 character should create a game. A level 70 character then joins. When level 70 character is in the game, level 60 character leaves. Level 70 kills everything. The game level will stay at 60 as long as host will remain level 60(which will be the case because he won't get any levels).
And as you said, Flawless Square gems stop dropping at level 61, so try not to get any experience with that level 60 character for as long as possible.