Awakening
Awakening was introduced 10/16/17 in the English version. About once per month, a previously released SSR kamihime becomes eligible for strengthening. By expending Draconic eyes on an eligible LV80 kamihime, the character’s upgraded form is unlocked. The character’s level and stats are reset to LV1 in the process, so the character is temporarily weaker until the levels are regained. As the character gains levels, existing abilities morph into upgraded versions, which is typically the most significant effect of Awakening.
The English version has roughly followed the DMM Awakening schedule of 1 Awakening per month, and also with the same release order.
Notable Awakenings (2/18/18; core SSRs): Gaia, Thor, Svarog, Titania, Ares, Sol, Hades, Satan, Uriel. Other SSRs are typically not worth Awakening unless you have an excess of shards or limited access to strong kamihime.
Awakening requires 3 Draconic Eyes (= 30 Draconic Eye shards), which are typically the limiting material. Additional Limit Break materials are required to reach max level once again. Limit Break material requirements can be viewed in the DMM version wiki. Note that these reflect reduced costs that were implemented in the DMM version; costs in the English version are currently considerably higher (as of 2/18/18). The reduced costs are expected to be implemented soon.
Draconic Eye shard sources
Weekly quest: 1/week
Advent events: 2 each (not always implemented in the shop)
Raid events: 2 each
Union events: 2 each
Duplicate Gatcha SSR kamihime: 10 shards per occurrence
A total of ~10 shards are available per month, so an active player capable of farming all content efficiently should be able to Awaken 1 kamihime per 3 months. Most players will have more Draconic Eyes than eligible SSRs to Awaken, or at least eligible SSRs that would be useful for them to Awaken.