There is a lady with a backpack on she gives you either a plume fossil(Archen) or a cover fossil(tirtouga)
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In the first bit of relic castle talk to the woman she gives you the choice of plume(archen) or cover(tirtouga) fossil
Go to Relic Castle and there is a lady with a backpack talk to her and she will give you a fossile choose the Plume Fossil for Archen,then go to Nacrene City in the Museum then talk to the lady that is just right from the entrance to revive your fossil
You don't get it from her, you get it from someone inside the Relic Castle. He'll offer you your choice from Cover or Plume fossils, Archen comes from the Plume one.
you have to get to the bottom
You can't you have to go to relic castle and on the west side of the B1F there is a pokemon explorer and she gives you whichever fossil you choose, choose the plume fossil and restore it a nacrene gym and out will come archen, you have to evolve archen to get archeops