From Destiny 2 Wiki
The currently-active challenges for Nessus can be checked by going to bungie.net, clicking on the magnifying glass in the upper-right corner, and searching for "Nessus".
1. Area Infiltration
- Lost Sectors: [region name]: Loot a Lost Sector near [region name].
- Nessus Scavenger: Gather [10 Datalattice / 3 Quantized Datalattice. [Harvest 10 Datalattice objects / Obtain Quantized Datalattice 3 times from harvesting Datalattice objects.]
- Treasure Hunter: Loot three Fallen or Vex supply caches.
- Event Horizon: Successfully complete a public event.
- Walk the Beat: Complete three Patrols. [Listed on bungie.net as Walking the Beat.]
3. Enemy Kills
- Scourge of the [enemy faction]: Defeat 75 [enemy faction] enemies.
- Cut Off One Head: Defeat [a / 3] Vex Hydra(s).
- Pikejacked: Steal a Fallen Pike and use it to defeat 20 enemies.
- Right in the Juicebox: Defeat 20 Vex with precision shots.
- Into the Labyrinth: Defeat 5 Vex Minotaurs.