The secret exit for Scourge of Armagon Episode 2 is found in HIP2M1: Ancient Realms. This is a written guide + images to find the secret exit, a video clip is also provided at the bottom if you prefer.
For this secret you must make your way through the level as normal until the very end. Instead of stepping through the normal exit gate, look above it for a shootable button.
Shoot it and head back up the stairs you came from. Keep following the stairs up and around to the right. You'll return to a room with red stained glass in the corner, drop down to the level below.
Turn around and there should be a raised metal gate in front of you, if not hit the button on the wall to open it again. Now jump on the metal gate itself and push the button on the wall (you may have already opened this secret earlier).
Turn right and you'll see a newly opened area, jump in and you'll find an elevator at the end. Use it but be careful as there are enemies at the bottom, you can either fight them or just run right past to the secret exit.