Prize Fights are key. Complete the reward track for weekend elemental to maximize essence shard haul. The 3 relics you get also come with shards, and a rare chance for a full crystal. The treasure nodes in daily Event Mode (Expert) also have shards.
Eventually I got strong enough to clear the 10% threshold in Prize Fights where one will get a regular supply of golds (some to raise, but most as material for diamond evolution).
If you do well in the elemental prize fight and do the master mode daily events, you'll get enough essence for 3 elemental essences in each of the 5 elements about 3 months.