You'll want to split the raid for this one. Kill order Urbaniok > Kulkak > Strixus. There are adds whom spawn throughout the fight, they do not do any dmg of significance, more of a nuisance than anything. They occasionally taunt the raid so have target macro's for the Princes.
All 3 princes have small aoe type spells (limited range 15m). If you're squishy I would suggest staying out at max range. None of the Princes have aoe auto so if you can survive the smallish aoe then go in FT.
Prince Kulkak the Ruthless
Hard hitting auto's, nothing special about this one
Prince Urbaniok the Just
Interupts need to be maintained or he will cast Justification (huge AoE dmg will one shot most classes).
Has a raid wide trauma based debuff (random targets). If it lands on a tank, make sure you have physical stoneskins/parry at the ready, it will enable the Prince to one shot you if you are debuffed.
Prince Strixus the Wise
Casts an incurable detriment on it's target group. Once the detriment has landed on all 6 members of its target group bad shit happens.
2 options here a) you can have a tank switch before that happens b) the incurable detriment is limited to line of sight (have a member of tank group out of line of sight of Strixus and you'll be fine)