Image: UbisoftOfficial screenshot from Ubisoft.
Back Home is the story trophy for the Lost Between Worlds DLC. You earn it by repairing Fai's vessel and escaping the Encasement, which means finishing the whole expansion.
Enter the rifts from the Encasement and clear them to recover the five Vessel Shards. Once you have all five, help Fai repair the vessel and escape.
Keep a stock of glints so a death late in a rift does not cost you the whole run. Remember that red and blue enemies only take damage from weapons of the matching color, so carry one of each.
Dani wakes in the Encasement after shooting Fai's crashed vessel. Fai, an alien consciousness, explains they are both trapped until the vessel is fixed.