Skittering Breach Stories

The story that's up for the day is on the main menu where you pick which tier you want. You don't even have to enter.

Shadow realm storyline:
As you enter and see the big Shadow realm portal at the entrance then you're as it says, in the Shadow realm story. This one is pretty straightforward.
Use the holy light dash ability to clear the void patches on the ground near the totems to dispel them and the immunity shield, kill the totems, then kill the final boss, where you can use the same tactic again.
I've attached the screenshots (if they get approved).

Renilesh Beckons storyline:
For this storyline you get from the start "Confront Speaker Xanveth" as an objective, you need to chase this boss 3 times in total to clear the delve, that's about it.

Old rituals Storyline:

If you encounter Lamplighter Havrik Chayvn at the start of it, then you're in the Old Rituals Storyline.
After you accept his quest then you just have to kill 3 Nerubian Ritualists and a minimum nr of trash mobs, and after that the final boss of the dungeon and you're done.

If you're doing this and are confused why you don't get the story shown, set the level to 4+. For tier 1-3 it is a set story.