Enter the bloodstained door behind the gate and search the area for resources. You can restock your Regenerative Vials with those on the ground, smash open the weapon rack and skull canisters for possible upgrades, or collect some gold from the treasure chest under the stairs. Climb up the stairs and watch for Wargar Zealots, followed by Wargar Guardians, who are determined to stop you.
At the top of the stairs, a Wargar Blastcaster or two will try to shoot down at you, with the remainder of their group hanging back in cover on the landing's other side. Pick off the Blastcasters at the top of the stairs from lower down on the stairs to avoid being targeted by the bigger Blastcaster group. Advance quickly up the stairs and duck behind the stone blocks ahead. You can't stay there long because of the Blastcasters' explosive arrows, though you might catch one or two moving for better position. If you're quick enough, you can snipe a few before they return fire. Failing that, E'lara can distract them with arrow fire while Caddoc uses Dash to smash into the closest one and disembowels the rest with his favorite pointy object.
You've finally made it to the bridge! Cross safely and enter the door. In the entry chamber, there are no enemies, so you can relax and use the obelisk or magic portal if you like. Take the stairs up to the door on the second level to penetrate the defenses even further.