Who choses the targets of the Exotrireme II's ability in Twilight Imperium?
The Sardakk N'orr chooses the targets.
This thread on BoardGameGeek has an official answer from FFG on the subject:

I do have another questions about some of the &quot;destroy abilities &quot; in game.
Exotrireme II - sacrificial ability , Assault Cannon, Yin Flagship.
1.) Am I correct to assume that for any Destroy ability sustain damage cannot be used ?
2.) Who select unit destroyed for Exotrireme II ability? Norr player or Opponent?

Hey Fedor,
Exotrireme— 1) That is correct, sustain damage cannot be used against
abilities that ‘destroy’. 2) The N’orr player selects the units to be
destroyed.
Let me know if I can help further, –––––––––––––––––––––––––––––––––
Dane Beltrami Game Developer dbeltrami@fantasyflightgames.com

This is also consistent with the &quot;Exotrireme&quot; upgrade from 3rd edition, which read:

At the end of a round of Space Battle, you may destroy 1 of your Dreadnoughts present to destroy 2 present enemy ships of your choice.