To free the chain in Inside the Mountain in The Journey in God of War: Ascension go through the orange lit tunnel until you get to some spikes:
Use the turning panel to the right to separate the spikes and go through the tunnel:
Use the orange patch at the top right of the spike wall to open the wall:
Go through and fight the enemies. Use the axe to lower the bridge:
Destroy the rope holding the big cart and push the cart so that it is level with the gap in the railing:
Climb the cart and go up to the upper walkway, go through the orange tunnel and destroy the planks:
Follow the tunnel all the way through and use the chain to raise the gate. Drop the chain and go down the chain. Push the large cart forwards until it lines up with the forwards upper walkway:
Climb the cart and jump over to the walkway. Go all the way to the end and lift the rock off the chain.