From Destiny 2 Wiki
The currently-active challenges for Titan can be checked by going to bungie.net, clicking on the magnifying glass in the upper-right corner, and searching for "Titan".
1. Area Infiltration
- Lost Sectors: [region name]: Loot a Lost Sector near [region name].
- Arcology Reclaimer: Kill 40 enemies in the New Pacific Arcology. [Only kills in the Arcology proper, inside the massive structure to the east of The Rig, count.]
- Arcology Scavenger: Gather [10 Alkane Dust / 3 Alkane Spores].
- Treasure Hunter: Loot three Fallen or Hive supply caches.
- Event Horizon: Successfully complete a public event.
- Walk the Beat: Complete three Patrols.
3. Enemy Kills
- Scourge of the [enemy faction]: Defeat 75 [enemy faction] enemies.
- Chain of Command: Defeat 5 Fallen Captains.
- The Grand Melee: Defeat 5 Hive Knights.
- Maleus Maleficarum: Defeat 3 Hive Wizards.