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