Here is the full list of all 14 Bridge Constructor Medieval achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Undercut crown budget by 1000.
Undercut crown budget by 3,000.
Earned 10 crowns!
Earned 20 crowns!
Earned 30 crowns!
Earned all crowns!
Score is 50,000 points or higher.
Score is 100,000 points or higher.
Score is 250,000 points or higher.
Plunged a total of 20 enemies into the abyss.
Plunged a total of 50 enemies into the abyss.
Rescued 15 of your own units from enemy fire.
Rescued 30 of your own units from enemy fire.
Built a bridge with at least 100 components.