Palkia is available in Pearl and Platinum (but only post-game in the latter). It can also be caught in the Ultra Space Wilds in Ultra Moon. While it can be caught in Omega Ruby, due to Nuzlocke Rules and the prerequisites of Uxie, Azelf, and Mespirit being in your party, it is illegal in a Nuzlocke.

Completed analyses of Palkia: