The album contains the full list of the Sidians currently available on the game, but to unlock the viewing here you must have had the Sidian at least once, it doesn't matter if you currently have it or you already sold/change it.
We have a list with all the Sidians we've found, so you can view it here
A mission is the prerequisite in order to obtain a Badge, and in most cases you need to simply max the level of the required Sidian, but also in some cases you can get it through special means, like events.
Collectible Story Edit
The collectible stories are side stories that you need to unlock to be able to read. They can be unlocked by having their respective Sidians at maximum level.
Student Body Election Edit
Once in a while there are elections coming to Sid and we all get to vote.
Mileage Ranking Edit
This tab is only available when a Mileage Events is active. If not you can see your past Mileage Ranking from the previous Mileage Event. Here you can check your current ranking on the event.