Borg 1 of 11
Officer shards can be earned by completing the following missions: And You Will Know Us... Part 1, The Fate of the Broken, To Err is Human, and What We Become. Additionally, shards can be gained through the Premium Officer Chest and the Ultra Officer Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests.

Borg 2 of 11
Officer shards can be earned through the Ultra Officer Chest and, occasionally, through the Rotational Ultra Chests.

Borg 3 of 11
Officer shards can be earned through exchanging Transporter Patterns and, occasionally, through the Rotational Ultra Chests.

Borg 4 of 11
Officer shards can be earned occasionally through the Rotational Ultra Chests.

Borg 5 of 11
Officer shards can be earned through the Ultra Officer Chest, the Premium Officer Chest, and occasionally, through the Rotational Ultra Chests.

Borg 6 of 11
Officer shards can be earned by completing the mission The Calm After the Storm. Additionally, shards can be gained through the Premium Officer Chest and the Ultra Officer Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests. You can also gather extra shards by exchanging Transporter Patterns.

Borg 7 of 11
Officer shards can be earned by completing the mission The Calm After the Storm. Additionally, shards can be gained through the Premium Officer Chest and the Ultra Officer Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests.

Borg 8 of 11
Officer shards can be earned through the Premium Officer Chest and, occasionally, through the Rotational Ultra Chests.

Borg 9 of 11
Officer shards can be earned through the Premium Officer Chest and, occasionally, through the Rotational Ultra Chests. 

Borg 10 of 11
Officer shards can be earned through the Ultra Officer Chest, the Premium Officer Chest, and occasionally, through the Rotational Ultra Chests.

Borg 11 of 11
Officer shards can be earned occasionally through the Rotational Ultra Chests.
 
Ghalenar
Officer shards can be earned through Borg Solo Armada Chests, by completing Special Events and in the Offers tab.
 
Borg Queen
Officer shards can be earned through Borg Solo Armada Chests, by completing Special Events and in the Offers tab.
 
Hugh
Officer shards can be earned through Borg Solo Armada Chests, by completing Special Events and in the Offers tab.
 
Dezoc
Officer shards can be earned through Borg Solo Armada Chests, by completing Special Events and in the Offers tab.
 
Gossa
Officer shards can be earned through Borg Solo Armada Chests, by completing Special Events and in the Offers tab.