Here is the full list of all 13 Ironclad Tactics trophies - there are 10 bronze, 2 silver and 1 gold.
Win "The State Dining Room" on NG+ difficulty
Complete the campaign on normal difficulty
Win "Baldwin Logging Camp" without attacking with ironclad weapons
Solve all of the puzzles in the campaign
Win "Mojave Desert" with a deck using only the "Native" faction
Win "Madame Millie's Ranch" after scoring at least 1 VP with a cow
Win "Factory-Fort Endicott" after holding both flags for at least one turn
Win "North Boulevard" after scoring 8 VP with the mortar
Destroy the warehouse sentry
Win "The North Lawn" without the Jefferson statue being destroyed
Embrace the future!
Win "San Bruno Mountain" on NG+ difficulty
Complete the campaign on NG+ difficulty