The following page describes Bekarna's Folly quest in Pillars of Eternity 2 Deadfire. You will receie the quest from Arkemyr in Arkemyr's Mannor (M32) on Periki Terrace (M15), but it can be done after completing The Archmage's Vault quest. Turing the quest, in search of notes, you will visit Bekarna's Observatory and you will encounter an old enemy from the first installment of the franchise.
First things first, you need to go to Bekarna's Observatory - she can be found on an island located to the north-east of Nekataka Island (the island can be seen in the above screenshot - market in red). Use a ship to get to the island and enter the observatory.
Once inside Bekarna's Observatory, head straight ahead - you will quickly stumble upon a group of mercenaries. It is worth to stick to the left side of the corridor, as it decreases the chance that your party will be flanked by the enemies located in the nearby room. The entire observatory is full of enemies. Start by taking out Corset, but pay attention to the shooters attacking your team from the elevation. Once you have defeated all of the enemies, you can start exploring the area.
Acquiring information about constellations
In the later part of the quest you will need information about four constellations - three notes can be found in Bekarna's Observatory, which is why you should acquire them right now.
Note - to acquire the knowledge from the notes, you must read them. Simply collecting them is not enough.
Right next to the place where you have met the mercenaries you can find stairs and a bookcase - The Huntress note can be found inside the bookcase.
Use the stairs and head straight ahead, until you reach a large archive. You will find The Kindfisher note inside one of the first shelves.
The last note in the Bekarna's Observatory can be found on the upper floor, near the entrance to the location. Use the stairs - The Leviathan note can be found on the bookshelf.
The last note can be found in the Planetary.
Bekarna's Observatory has one additional location - the Planetary. The entrance to it can be found to the right of the place where you have met the mercenaries.
The Planetary is a small location - follow the only possible route until you reach an enemy from the first installment of the franchise, Concelhaut. This will initiate a conversation, but regardless of your choices you will end up fighting the man. First things first, focus your attention on Concelhaut - he is a powerful mage, capable of dealing large amount of damage. Once he is dead, you should search his body to acquire his unique pet.
Once all the enemies are defeated, search the nearby desk - there you will find the last notes called The Panther. There is a telescope located right next to the desk, but you need to wait for the night to use it. Rest your party to speed up the time. Afterwards, activate the telescope and use all of the dialogue options (remember that you need to read all of the notes about constellations - otherwise the options will not be there).
Now head back to the Planetary and stand at the entrance to the location. Approach the control panel and activate the Planetary. You will see a short animation, after which you will be able to acquire Bekarna's Research.
Meeting the Archmage's Circle
Once you have acquired the notes, you can head back to Arkemyr. He will be waiting for you at Arkemyr's Mannor (M32), but this time you will find him in the lower part of the building, inside the room with scrying pool. Approach the pool shown in the screenshot and activate it.
This will initiate a paragraph scene - select the option to dip your face in water to continue. You will join a conversation with the Archmage's circle. It does not matter what dialogue options you will select here. Once the dialogue is over, you will complete the mission and receive your rewards - an unique grymuar Incredible Discoveries of Akemyr and 5,000 gold.