Where is Omega Pirate in Metroid Prime Origins?

Omega Pirate is fought in Elite Quarters (Phazon Mines). Beating it gets you: Phazon Suit.

How to get there

Starting a new game from Landing Site, get these first, in this order, then go to Elite Quarters (197 rooms in all):

1. Missile Expansion in Landing Site (0 rooms; needed for Elite Quarters (Missile))
2. Space Jump in Alcove (1 room; needed for Elite Quarters (Space Jump Boots))
3. Morph Ball in Ruined Shrine (10 rooms; needed for Elite Quarters (Morph Ball))
4. Power Bomb Expansion in Magma Pool (6 rooms; needed for Elite Quarters (Power Bomb))
5. Morph Ball Bomb in Burn Dome (11 rooms; needed for Varia Suit (Morph Ball Bomb))
6. Varia Suit in Sunchamber (10 rooms; needed for Elite Quarters (Varia Suit))
7. Charge Beam in Watery Hall (7 rooms; needed for Wave Beam (Charge Beam))
8. Wave Beam in Chapel of the Elders (27 rooms; needed for Ice Beam (Wave Beam))
9. Boost Ball in Phendrana Canyon (8 rooms; needed for Ice Beam (Boost Ball))
10. Super Missile in Observatory (10 rooms; needed for Spider Ball (Super Missile))
11. Spider Ball in Quarantine Cave (9 rooms; needed for Ice Beam (Spider Ball))
12. Ice Beam in Antechamber (39 rooms; needed for Elite Quarters (Ice Beam))
13. Grapple Beam in Storage Depot B (18 rooms; needed for Elite Quarters (Grapple Beam))
14. Plasma Beam in Plasma Processing (15 rooms; needed for Elite Quarters (Plasma Beam))