You access Tanzan Depths when the player gets teleported here. The player and Saphira (also Laura depending on your choices) try navigate through here only to get ambushed by a Steelix. After defeating it, Saphira takes you out of the depths for you to exit. You can return here through the cave next to the Meteor Base.
You can also access the Tanzan Depths by using Rock Climb from the middle of the Lake in the Hidden Cove south of Charlottes House, upon entering it will say the ground is unstable. You can get The field effect note for Flower Garden.
After destroying the meteor base, go back to where you first woke up in Tanzan Depths. There will be a Seviper there licking the acid. Interact with it and it will battle you. The Seviper will have either Stockpile, Body Slam, or Final Gambit as its egg moves.
If you use Earthquake or Bulldoze in the area with the field effect note, the ceiling collapse will open another Rock Climb area with a Larvitar. Complete the puzzle for a chance to battle it. The Larvitar will have either Dragon Dance, Curse, Iron Head, Outrage, or Stealth Rocks as its egg moves.