The journals are marked in the map so you just need to head to their general locations and collect them. They can be collected in any order you please.
1. Under Blake Bridge
2. In a boat, docked by a shack to the uphill lake north of The Highlands – Extraction Point
3. Frothing Creek Mill, inside a parked van
4. Aggregate Acquisition. This is a hyperion base and the journal is found in a room on a roof of the marked building. To reach it, you have to find the uphill path to the northeast then cross the bridge west, destroying the constructor along the way. Follow the path to the southwest until you reach the room.
After collecting all journals, return to Tannis to complete the mission.