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These are the bosses of the 3rd area of the game, and involve a lot of mid-air combat.

The big crystal between them is their "core", and you must destroy it to deal damage to the boss.

I advise having a high damage stat, and perhaps using the Deathblow perk (increases Finisher damage at the cost of maximum energy).

Other than that, just fly around the arena and fight them. Whenever one is stunned (damaging their Elder Shard Fragment until their health drops to 0), you can damage the main "core".