It is basically luck. I have one game that is still missing two (uncommon!) beetles and one gold pebble.

I keep my game focused on the gong encasement and use the '8' and '3' buttons a lot to keep checking the other area.

I've found that if I pay more attention to the collectibles while finisihing the puzzles I had better luck at completing all of the collections earlier. But eventiually, the ones I need show up.