There are two possible ways to get through this tunnel. I've written from the perspective of having gotten permission from Gregory in Lorelei, Midori Province, but if you haven't you can fight your way through the first section.
When you first enter you should enter the inn just to the northwest of the Portcullis and talk to the innkeeper. This is Velasquez, and as well as running the inn he'll give you information on the tunnels and sell a few items.
Velsquez will tell you about a lever off of his office, so enter his office, which is the southern of the two doors on the eastern wall. The lever is in a secret room which can be entered through the wall just to the south of the bookshelves. Pulling this lever solidifies a bridge in the tunnels.
Now leave the inn. If you want to, and have a decent enough tool use skill you can enter each of the three doors in a building to the east of the inn. Each room is guarded by a Basilisk, and the chests are fairly heavily trapped. Save your game before entering the rooms. If you're successful in disarming the traps you'll end up with a few nice items, including a suit of Blessed Plate Mail and a Firewalkers Band.
Now head north of the inn to a bridge. Before crossing the bridge look to the west to see a passage leading off that way. The first room has a barrier in it, which you'll need Dispel Barrier Lv.2 or a Piercing Crystal to get through.
Follow the passage until you reach the bridge leading over a chasm. If you pulled the lever back in the inn you can cross over it. If you haven't, there's a secret passage to the south which leads around the chasm, but you'll need Move Mountains Lv.3 to get through it.
Continue following the passage and you'll eventually come to some Spine Beasts. Kill the Spine Beasts and continue along the passage until it opens up into a large room.
In the large room is a Doom Guard, which will probably take a little bit of effort to get by.
Once you've killed the Doom Guard go out the portcullis to the west. Take note of the wheel in the small antechamber. When you return through the passage you'll have to use this wheel to open the portcullis.
Going up the stairs will take you into Blackcrag Fortress.