To start the Tribute to the Past quest, go to Saint-14 near his ship in the Tower hangar.
Early colonies
You need to visit Titan and destroy 100 enemies. I recommend taking part in open events - for example, the Witch's Ritual, as there will be many enemies. Also a great option would be Lost Sectors.
Lost colonies
Visit Exodus Black and then speak with the Neuromatrix on Nessus.
Memory by ministry
You need to complete three tasks on Nessus:
Military casualties
Travel to the EDZ and speak with Devrim at the Church in Trostland. Then complete the following tasks:
Fortunately, outdoor events are common in Trostland.
Return to Saint-14
Return to Saint-14 in the Tower and he will ask you to place a Tribute to the Past memento in the dwelling near his ship.