This is by far the easier one between this and the Hive.
First off, people need to stop saying something "sees through invis", when that creature is actually undead. A mob that sees through invis sees through whatever type of invis would otherwise affect that mob. It's as silly as someone saying "that mob sees through IVU!!!". Well duh.
Understanding this, the only mobs that actually see through invis are the water creatures in the various tunnels. This means that the only way to get two the two locations up in the back area (Conclave and Audience Chamber) is to use levitation. Just make sure you've got one ready and it's a piece of cake.
Best way to do this is to hit the "outside" ones first. Using normal invis, swim down to just outside the Infested water cave to get that one (you don't have to enter or come within agro range of anything). Ditto for the Arena, although keep an eye out of occasional undead that'll pop out just on the outside of the wall. You just need to get right near the wall at the right spot to trigger the task stage. I say do this with invis because there are some non-undead mobs swimming around in the water.
The statue and Citadel are super easy. Just swim out of the water near the taskgiver guy (should be out of agro of everything there). Use IVU. Run up the hill to one of the tower entrances (I entered at the West side where the broken bridge is). Drop down and go inside. Every single mob in there is undead. Coming from the west, you go into the main chamber, hang a right. Go up the ramp. Walk in a short distance and get statue stage. Turn around and go back down ramp. Go straight north through the door and across the bridge to the citadel. Enter, hang a right, go up a ramp. Citadel done. Reverse direction and come back out.
For the last two simply Cast levitate and head directly across to the wall to the right of the broken bridge. As described elsewhere, with levitate you can work your way up that wall and then to the left and drop onto the end of the bridge. Stay to the left side as you travel around since there are some deep orcs in the tunnel entrance (where you would have come in if you'd gone through the infested cave). Cast another IVU and head in. Once again, all mobs are undead. They don't "see invis". They are undead. Use the correct invisibility and it's trivial. Just avoid the named mobs and it's a piece of cake. The instructions a couple posts below this are perfect.
I did all of the Slipgear tasks using nothing but cloudy potions and IVU. There is no need for shrouds if you don't feel like it.