Once you have bought each weapon (idols are not required) you will have to play with each. Without exiting the game. Even if you have the 4 individual achievements for each weapon class done before.
But similar to the other 4 weapon achievements you can simply start a level and exit right away. So you will have to do this 16 times without exiting the game.
For the crystal shards I found the green ones to be the rarest but it's not like you have a choice what you get. You get most shards after defeating the final boss. But you will also get some in the earlier stages as well. Just to give some rough guidance: I finished world 1 (Spookem) 17 times, world 2 (Ice Queen) 6 times and world 3 (Kult Overlord) 5 times until I had enough shards. Additionally I had some rund where I didn't finish the world.
This game is best to be consumed in small doses. I start the game everyday and check the missions. Usually there is 1 or 2 that I can do. And it gives some shards along the way. I am 29/37 missions completed when I unlocked this achievement here.