Here is the full list of all 13 Ironclad Tactics trophies - there are 10 bronze, 2 silver and 1 gold.
Complete the campaign on NG+ difficulty
Win "San Bruno Mountain" on NG+ difficulty
Win "The State Dining Room" on NG+ difficulty
Win "Baldwin Logging Camp" without attacking with ironclad weapons
Win "Mojave Desert" with a deck using only the "Native" faction
Solve all of the puzzles in the campaign
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 "The North Lawn" without the Jefferson statue being destroyed
Complete the campaign on normal difficulty
Win "North Boulevard" after scoring 8 VP with the mortar
Destroy the warehouse sentry
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