First of all - Don't hit the Solve button when it becomes clickable.
Place all cards into the foundation with the exception of Jacks, Queens and Kings.
You won't be able to place all three (Jack, Queen and King) cards of the same suit into the foundation just like that. To do it you need to "reveal" them first, so that they're on top of the stack.
So say you want to place suit of hearts into the foundation. Leave that suit intact and place all other cards that you can into the foundation. Then all three cards should be "on top" and you can place them in the order of Jack, Quen and King into the foundation.
The achievement took 15-20 seconds to pop for me, so if you're unsure just wait and if it won't pop up, just hit undo and try again.