To unlock the Survivor trophy in Assassin's Creed Liberation Remastered, you will need to kill 10 alligators in the Bayou.
You will be given a tutorial on how to defeat alligators during sequence 2. For the trophy, you won't need to collect the eggs, simply killing them is enough. You can visit the same nests repeatedly as the alligators will respawn there once they have been killed. Killing them again will still count as progress towards the trophy.
Once you have defeated 10, the trophy will unlock.