You will be taken to the headquarters of the Aether Foundation by ferry. Upon arrival, you'll be at the docks area. Faba will take you to the lift, before leaving you in the hands of an acquaintance. From here, you'll be shown the entrance area.
Finally, you'll end up in the conservation area. It seems the president of the Aether Foundation is here, so this is a good chance to say "hi". Before continuing though, if you don't mind taking a short detour, go forward and use the lift controls.
Select "B1F: Docks" to return to the docks sea. Here, head north-east between the two group of boxes. Go behind the boxes on the left to find a delectable Rare Candy waiting at the end. That's everything, but if you're curious, you can look around the rest of the facility as well.
Most areas are off limits though. Once your curiosity is sated, return to the lift and select "2F: Conservation area". Back upstairs, follow the path south-west towards the far corner. Next, head all the way north, along the west-most side. Hmm, doesn't this place look awfully familiar?
At the far north-west corner, make your way east. Be sure to set a Ground or Water-type Pokemon in your first slot. As you reach the middle of the northern path, you will find the president. Afterwards, a mysterious creature will make an appearance. Continue east to battle it.
Whoa, what exactly are we dealing with here? Is this even a Pokemon? Well, Pokemon or not, the battle functions similarly to a battle with a Totem Pokemon, except the mysterious creature does not summon allies. At the start of battle, it will receive a big Defense boost from its aura.
It is Rock and Poison, so Ground moves do 4x damage. Water, Steel and Psychic moves work well too. Steel-types are also good since they're immune to Poison. If you have one, Dugtrio is probably the best bet here since it's Ground and Steel.
After that otherworldly encounter, you'll be escorted back to the ferry, ready to continue your island challenge. As a souvenir of your time here, you'll receive TM29 Psychic.