Here is the full list of all 36 Spice Road achievements.
Defeat all enemies on "Art of War"
Complete all mission objectives in the Campaign
Complete Mission 20 on Hard Mode
Complete the entire Spice Road Campaign
Complete Mission 19 on Hard Mode
Complete Mission 18 on Hard Mode
Build a Factory
Build a Hospital
Complete Mission 17 on Hard Mode
Build a Fortress
Build a Cathedral
Build a City
Build a Theatre
Complete Mission 16 on Hard Mode
Complete Mission 14 on Hard Mode
Complete Act 2
Complete Mission 13 on Hard Mode
Complete Mission 12 on Hard Mode
Build some Apartments
Complete Mission 10 on Hard Mode
Build an Inn
Complete Mission 9 on Hard Mode
Build a Slave Market
Complete Mission 8 on Hard Mode
Complete Mission 7
Complete Act 1
Defeat a whole Faction
Defeat all the Bandits on a map
Complete Mission 3
Complete Mission 2
Create a Trade Route to another Settlement
Achieve 100% Popularity in a Town
Build a Town
Create a Trade Route to a Supply Point
Discover a Resource on the map
Build a Campsite