This is one of the hardest artifacts to get mainly because it's a timed run to get it.
When you pull the switch, a pole will come out of the wall and you have 90 seconds from that point to get to it. You need to get to the top flawlessly in order to reach it.
You should make a save here and if you don't make it, try again.
When you reached it in time, swing across and pick up the artifact.
There it is: artifact #1.