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.
Built a bridge with at least 100 components.
Earned all crowns!
Plunged a total of 50 enemies into the abyss.
Plunged a total of 20 enemies into the abyss.
Earned 30 crowns!
Score is 250,000 points or higher.
Earned 20 crowns!
Rescued 30 of your own units from enemy fire.
Rescued 15 of your own units from enemy fire.
Earned 10 crowns!
Score is 100,000 points or higher.
Undercut crown budget by 3,000.
Score is 50,000 points or higher.
Undercut crown budget by 1000.