After you beat the elite 4, go to celestic town and talk to the elder. Bring both the adamant and lustrous orbs to spear pillar.Plz send feedback!
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After you catch Giratina, go to Celestic town and back to the Spear Pillar. A blue or purple cristal will be floating will be seen. The blue or puple crystal will be Dialga or Palkia. To catch the next one leave Mt. Cornet and re-enter Spear Piller. The next Dialga or Palkia will be there. I only say Dialga or Palkia because I don't remember which one comes first.
Palkia is bad and dialga is good
You can't get Dialga and Palkia in Emerald.
palkia
You can catch Palkia in Pearl and tranfer Dialga to pearl from diamond.