Take the ladder back down before retracing your steps until you reach the roof, with the crumbling pillar on Elden Ring Runes it. There will be the gap between this roof and the one on which you took on the stormhawk. Repair to full HP, then proceed into the courtyard below, where you will find an Stonesword Key door and a Somber Smithing Stone. Utilize that Stonesword Key you recently got to open the door, but be careful of the two axemen waiting inside. Bring them into the courtyard one at a time when you're in need of a little distance to avoid. They are extremely slow, meaning you can easily get bnehind them and use a back stab. In the room, you'll see three weapons: the Hawk Crest Wooden Shield, Misericorde, and the Iron Whetblade.
Back into the courtyard and enter the second door you've not explored yet. Inside is a dining hall secured by a Grafted Scion, but we don't wish to confront it just yet so run across the room and enter the tiny room on the opposite side. There are two dogs and an animal called the Crimson Hood atop a pile of bodies.
Then exit the room and go into the door on the left. Here you will discover the elevator that will take you back onto the Spot of Grace.
If you're short of Flasks you can take a break, but we still have the chance to jump a bit more to do. Retrace your steps to the top and then jump over the towers. Then return to the roof with the crumbling pillar. Make your way up the hill like you're returning to the rooftop from where you obtained the Claw Talisman. But instead, descend to the platform below you before dropping down onto a huge open rooftop with two soldiers in the distance. Infiltrate behind the weaker one and then backstab them, so you can take on the halberd knight one on one. As before, your approach is to strafe in an attempt to buy Elden Ring Runes make a backstab and then counter the attack when you detect an opening. Just keep in mind that the majority attacking patterns have two components, so don't over-attack too quickly.