Here is the full list of all 39 Sailing Era achievements.
Win a battle by bringing down the flagship of a fleet
Complete Andrew's Main Quest: Chapter 2
Unearth 10 treasures
Bring down 1 enemy ship with a ram
Establish 3 commerce guilds
Reach Max Contribution at 1 port
Complete Andrew's Main Quest: Chapter 1
Force all the enemy ships into surrender in a battle
Gain a flawless victory in a Hand-to-Hand Combat
Obtain all the trophies
Complete Andrew's Main Quest: Chapter 3
Complete Andrew's Main Quest: Chapter 4
Complete Abdullah's Main Quest: Chapter 1
Complete Abdullah's Main Quest: Chapter 2
Complete Abdullah's Main Quest: Chapter 3
Complete Abdullah's Main Quest: Chapter 4
Complete Yoshitaka Shizuma's Main Quest: Chapter 1
Complete Yoshitaka Shizuma's Main Quest: Chapter 2
Complete Yoshitaka Shizuma's Main Quest: Chapter 3
Complete Yoshitaka Shizuma's Main Quest: Chapter 4
Complete Yun Mu's Main Quest: Chapter 1
Complete Yun Mu's Main Quest: Chapter 2
Complete Yun Mu's Main Quest: Chapter 3
Complete Yun Mu's Main Quest: Chapter 4
Bring down 1 enemy ship with a single round of shooting
Bring down 1 enemy ship with naval mines
Discover all the fisheries
Discover all the ports
Discover all the waters
Complete 10 bounty quests
Fulfill 10 business contracts
Salvage 10 shipwrecks
Earn 1,000,000 in profit from a single transaction
Reach Max Favorability with bar girls at all the taverns
Reach Level 99 with 1 character
Obtain every unique equipment
Unlock 40 routes
Sail for 100 days in a row
Explore for 100 days in a row