Master of ChronosG 10

Once you've unlocked the Mystic Ruin, you can begin exploring it with the hope of finding treasure. Each expedition comes with a recommended 3 dragons which change each time you find a chest. Sometimes you'll have the dragon, sometimes you won't. It's important to choose your expedition dragons first before setting any dragons to breed, since a dragon can't do both. If you have no active breeding missions, focus on unlocking dragons that the ruin is recommending, since even with 2/3 recommended dragons, your chance of success is lower than 50%. With all 3 recommended dragons, it goes up to 100%.

Chests will randomly contain Shards, and there is no way to manipulate the drop rate. Your best chance is to just have as wide of a variety of dragons as possible to be sure you can always send all 3 recommended dragons, and always be searching the ruins. It costs nothing, and even if your expedition fails, you still get SOMETHING, so you might as well keep it active whenever possible.