Sky Pirate's Den is a section under Clan Primer, where prizes for various achievements are stored. These prizes have form of things/people/monsters that appear in the game. Additionally with every figure you get a title. Here is the list of every prize you can get in the game in the order from the easiest to the hardest one to get (in my opinion):
How to get it?
Steal from enemy over 50 times
Attack over 300 times
Use magick over 200 times
Defeat over 500 foes
Use technicks over 100 times
Take over 50 000 steps
Sell over 1000 pieces of loot
Earn over 100 000 gil
Kill over 50 enemies in a chain
Spend over 1 000 000 gil
Raise the average level of the party to 50
Get 500 000 clan points
Get to know every techinick there is
Get to know every magick spell there is
Master everyone's License Boards (including Espers and quickenings)
Perform every concurrence (See section "Quickenings")
Buy Canopic Jar (see section "Bazaar / Grimoires")
Defeat "Trickster (rank V)"
Defeat "Carrot (rank VII)"
Defeat "Ancient Man of Mystery (rank VII)"
Defeat "Deathgaze (rank VII)"
Defeat Ultima Esper
Defeat Zodiark Esper
Get every Esper
Defeat "Fafnir (rank VII)"
Lord of the Kings
Defeat "Behemoth King (rank VII)"
Defeat Hell Wyrm (see section "Bosses not connected with the plot")
Get every map and visit every location in Ivalice
Defeat "Yiazmat (rank VIII)"
Defeat every monster which prowls in Ivalice the required amount of times