The best way to get Dragon Gems without buying them is to tap Dragon Stars, so we'll need to farm them in levels. As they appear randomly it's almost impossible to gain 3 Dragon Stars in one level, and thus you probably won't be able to merge them in a level. Luckily you can take them home to your Camp if they appear in a level by leaving them alone until you finish the level (you can also almost always tap the purple star once for a freebie gem prior to exiting the level). Your Dragon Star(s) will show up as a free reward when you collect your level rewards, and you'll need to select it by tapping before leaving the rewards screen. At your camp, you can then merge 3 (or even better: 5) of them to gain a Magnificent Dragon Star and tap it for about 5 Giant Dragon Gems, which you should definitely merge in 5s, as the level-3 gems only give exactly as many gems as 3 level-2 ones.
How to get the most profit from your stars:
From the moment the star appears, it is determined how many times you can tap it. So, don’t do it in the level as you can’t merge it there. Once in camp, you can keep the level rewards with the dragon star bubbled until you have 5, this way you won’t accidentally tap it. When you have 5, you unbubble them and place them close to each other, ready to be merged. The number of times dragon stars can be tapped is random. It varies between 1 and 3 times before they turn into the regular yellow stars. With the following trick you can find out how many times. Fly to the map, disconnect with the cloud and go back to your camp. Like this your actions won’t be saved. You can now safely tap your stars and count how many times you can do each one. Make sure to remember it! Then you fly back to the map, connect and RETRIEVE the previous save. Pay attention to not chose to keep playing! Now the game is reset to before you tapped your dragon stars, but you know how many times they can be tapped. If that was for example 3, you can tap it 2 times. Don’t merge them yet. Now you connect and chose to keep the current game. A Magnificent Dragon Star can be tapped 7-11 times for gems. Again, you can use the cloud to get as many as possible. Disconnect to the server, merge the dragon stars and start counting how many times you can tap them. If you want more taps, connect again and retrieve previous cloud save, disconnect and do it again. This only works if you merge your dragon stars after you disconnect to the server. Now you can merge the gems by 5’s.
Cosmos Dragon Eggs
Of course you can wait for Cosmos Dragons to randomly spawn from merged Sapphire Eggs, but you could also just play one level over and over, as you'll get Cosmos Dragon Eggs and Nests as Level Rewards if you finish it a certain number of times.
At first, you play a few times (usually three times) for a chest (often a Dangerous Chest). Then you play for a Cosmos Egg. When you have achieved the single egg, you play for a nest of Cosmos Eggs. A nest can contain as many as seven eggs, and no fewer than three eggs. When you have achieved the nest, the cycle starts again, sometimes with a different type of chest. Each time you complete the entire cycle of chest, single egg and then nest, the number of times you are required to play to gain the reward is increased. If you play the same level too many times, the chalice cost of gaining the reward and the time involved outweighs the actual reward itself, making the level only useful for Dragon Star farming.
Each level also lists "possible rewards". These are randomly offered to you for free in the level rewards
when you complete the level, and include a Dragon Egg for a particular type of dragon. The egg is quite infrequently offered, and (as with all level rewards) you need to tick it to bring it back to camp.
This is distinct from eggs that are offered in the level rewards at the cost of gems. The "possible rewards" eggs do not need to be present at the end of the level, whereas eggs that can be bought in the level rewards are simply objects that were lying around when the level completed.
"Possible rewards" eggs are an added (and welcome) bonus for repeatedly playing a single level.
Obviously you're rewarded pretty well for finishing levels many times, but most of the levels take a huge amount of time and also require to plan your merges ahead to get all 3 star objectives. While most gem farming is done using Dread Marsh 3, Zomblin Falls 1 and Skull Grove, there are many levels that have proven to be quite fitting for farming Dragon Stars and Cosmos Dragon Eggs.