Use the stairs, what takes you to the big room. Garrett will meet here monsters, identical with those you've met in the old prison. On the upper level, you run into three creatures and you can eliminate the at once if you want to. I recommend to throw something heavy at the first one and then encourage the remaining two with a throwing device to stand where the oil spilled . Shot there with a fire arrow and the monsters are done.
Killing monsters isn't obligatory, because you can reach the exit without meeting them. Theoretically, you'd be able to walk on the main bridge, but it'd be very risky and you'll have to move very slowly to avoid being detected by the monsters. But if you want to do it even so, move east where the exit from catacombs is.
The much better idea is to go through the bottom level. Especially, that there is a lot of new treasures you can get. Reach the northern stairs to get onto the bottom level. When you get to the end of the stairs, turn right and jump over a small hole. It takes you to a small shelf under the bridge. Here you can find Ring - 14G. Return to the stairs. If you want to continue journey through this part of catacombs, you'll need to use Rope Arrow. It'll let you reach the eastern shelf. Here you can open northern door with lock-pick. Enter the small room and use Wirecutter on the chest and only then look into it and take an Ancient Vessel - 48G and The Mortal Coils - Bronzehead Bracelet.
If you have used a Rope Arrow, move east after exploring this room. There you can grab new unwound line. If you don't have Rope Arrow or you don't want to use it (you can get to the described room also from the eastern side) you can choose the whole different path. Begin on the upper level in the beginning point and move east, passing the first monster from the east. Turn at the first possibility south and find a place where Garrett may jump onto the lower shelf. Repeat the same again, what takes you to the bottom level.
On the bottom level of the catacombs you get choosing the northern (with Rope Arrow) or southern (jumping down) path. You have to be very cautious in here, because in the northern room you find a single monster. Nevertheless, search this place (move SLOWLY), because you find here Pile of Coins - 20G. You can reach now the eastern part of the upper level of catacombs by grabbing the unwound rope and climbing up. It lets you omit the main bridge and approach the catacombs exit from the northern-west side.
You're going to the closed gate shown on the screen above. By default, it's guarded by two monsters. Try to get closer to them from the side which is less defended at the time. Move slowly. A good idea is to use a throwing device to get them off the exit. If you expect troubles, use the button on right from the gate, what turns the light FOR A WHILE. When you think that it's safe enough, use the switch to rise the gate and leave this area [The Hidden City - Catacomb Shaft].