Here is the full list of all 60 Expeditions: Conquistador achievements.
Capture Xochiyohua
Rebuild Fortaleza De Gutiérrez
Find all the cairns and compile all the maps of Mexico
Kill an enemy unit with a cannon blast
Discover El Dorado
Discover the Masaya Volcano tunnels
Aid the escaped slaves
Inadvertently unleash smallpox on the population of Tenochtitlan
Recruit Anacaona for your expedition
Achieve a Flawless Victory in an Escape battle
Sacrifice a member of your expedition
Discover Tenochtitlan
Marry a native
Deal more than 100 points of damage with a single attack
Enter combat with six units at Veteran or higher rank
Cast off for the mainland!
Find all cairns on Hispaniola and compile all the maps of the island
Complete 5 side quests in Hispaniola
Revive an incapacitated unit and keep that unit alive until the end of the battle
Save Governor Bernardo De Manzanedo
Kill an enemy with an Interrupt attack
Hit one of your own units with AoE damage
Enter combat with at least 25 points of Equipment assigned to a single unit
Nurse a Fatally Injured expedition member back to full health
Defeat Esteban Gallego
Score a hit with a ranged attack with a 5% hit chance
Complete The Gloaming
Win all three battles in the Tournament
Win a non-tutorial battle without ever getting within melee distance of an enemy
Have all your followers be disabled at the same time
Resolve the Jungle Drums goal without bloodshed
Recruit Isabela de Yruenes for your expedition
Kill an enemy with a flanking strike
Lose the first tutorial battle
Attack and destroy a native settlement on Hispaniola
Kick off the battle for Tenochtitlan
Kill Moctezuma Xocoyotzin
Save Moctezuma Xocoyotzin
Turn against your allies in their hour of triumph
Form a romantic relationship
Restore Fortaleza De Gutiérrez to its full glory
Discover the Fountain Of Youth
Complete The Temple of Death
Achieve fifteen Flawless Victories in a row on Normal or greater difficulty
Win a non-tutorial battle with only Scholars and Doctors
Kick an enemy into a burning or trapped space
Complete the game on Normal difficulty
Complete the game on Hard difficulty
Complete the game on Insane difficulty
Complete the game in Iron Man mode on any difficulty
Return to Spain with 50,000 Valuables or more
Return to Spain without losing any expedition members
Unlock all the Codex entries
Fully research all the possible inventions and construct one item of every possible recipe
Start the game with only women, as a female character
Recruit all 6 native followers in Mexico in a single playthrough
Trade at every market in both campaigns in a single playthrough
Experience a mutiny
Make camp without giving any of your followers food
Promote a follower to Lieutenant