Here is the full list of all 36 Spice Road achievements.
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
Build a City
Build an Inn
Build some Apartments
Build a Slave Market
Build a Fortress
Build a Hospital
Build a Theatre
Build a Cathedral
Build a Factory
Defeat a whole Faction
Defeat all the Bandits on a map
Defeat all enemies on "Art of War"
Complete Mission 7
Complete Mission 8 on Hard Mode
Complete Mission 9 on Hard Mode
Complete Mission 10 on Hard Mode
Complete Mission 12 on Hard Mode
Complete Mission 13 on Hard Mode
Complete Mission 14 on Hard Mode
Complete Mission 16 on Hard Mode
Complete Mission 17 on Hard Mode
Complete Mission 18 on Hard Mode
Complete Mission 19 on Hard Mode
Complete Mission 20 on Hard Mode
Complete Act 1
Complete Act 2
Complete the entire Spice Road Campaign
Complete all mission objectives in the Campaign