The second relic is in the room with the spikes. In order to get it, you need to to a jump to the ledge on the left wall.
It's not really about skill here, but more like about luck ... so with a few save/loads you should get it right.
Get into the enclosure and the artifact #2 is yours: the Athenian Owl Figurine.
The use your brains method (thanks to Gogolu):
Use the box you moved to get access to the switch and bring it to the main room.
Move it next to the pillar closest to the relic.
You can first flip the switch that raise the pillars and then move the box, it might be easier to spot which is the pillar you're looking for, either way, you'll need to have the pillars up then place the box with a corner in the crumbled section.
Then you go back up, repeat the steps you did to get to the lead bar, but instead of jumping to the enclosure, this time jump to the slope and then to the ledge ahead.
There you have it.
« Relic #1