This is to help people; I figured out some interesting tips and I wanted to share exactly how I beat these two missions on singleplayer Heroic. Reply with your tips and comments if you want.
Use weapons with 1.5x undead damage and it will be much easier.
For the sappers, you just have to know which direction they're coming from. In the first sapper level they will come from the far end first and the near end second, and you get a few seconds to run to the other side. If you stand close to the mouth of a bridge they will funnel into it and make for easy shooting. In the last sapper level they spam you from all directions, so just learn to hit the roll button whenever one of the sappers lights himself up. It's weird how they can one-shot you if you're standing right next to them but if you roll you don't really get damaged at all.
Kills the trolls before they enter the arena using a high-powered shot like Andriel's exploding orb.
Each time a wave ends have everyone huddled in Sanctuary to restore their health.
You can buy yourself time by beheading the undead archers and letting them wobble around, then killing them when you are all set and ready for the next wave (it's like creating a crawler on CoD's zombies level so that you can run around and board up the windows).
Hide in a corner of the map at all times and gather your friends around you. That way you can't be hit by archers or sorcerers until you're done dealing with the melee attackers. It also slows down the attack and decreases difficulty since the enemies will sometimes come one by one and because they will be funneled into a narrow corridor for easy shooting. It also means that you are right next to one of the four chests.
You can use the block function to great effect up until the hammer troops show up. I got to wave ten with a level 11 mage simply by blocking and using periodic staff blasts while surrounded by vast numbers of orcs. Once you get to a point where you can no longer just block/kick and stand in one place, you've got to sprint. You should make a circuit around the arena's corridors, only going into the center to switch to the other side of corridors, then turning around to blast the chasing enemies. After a while they will all be dead.
This works like a charm, especially when the sappers come. As soon as it gets too hot and your companions are dead, just start running and you will gain a tail of sappers that you can quickly turn around and pick off. Remember to roll whenever someone tries to cut you off. Once you've run around the entire map a few times they should all be in a single group right behind you.
Level 15 is the hardest because it is the only level where it might be impossible to do the above strategy. You have to be very careful and make sure that two or more Orc Chieftains don't get into the same group. In this level your partners are going to die after a minute or so and you will end up being chased by the rest of the enemies around the map, doing a circuit just like I described above. But for some reason, Orc Chieftains seem to heal and/or protect the orcs around them. This usually isn't a problem - if you knock out the chieftain you can knock out the rest of the troops, since they can't heal/protect themselves. But other chieftains can the chieftains. Once I was running the circuit on Wave 15 with the mage and had two Orc Chieftains on my tail with a gaggle of hammer orcs. I blasted them all with every spell in my arsenal for a good 15 minutes and not a single one died. When I tried it later and there was only one chieftain to contend with, he took a couple of blasts and then fell. I have no evidence to prove that they somehow make each other invincible besides this and the story of another gamer on the net who also described how the group of chasing orcs became invincible and forced him to give up. The last level with the trolls is easy compared to Wave 15.
After each wave remember to push the down arrow (several times) to recall your companions into the hallway, sort of "resetting" their positions for the next wave (and use Sanctuary for free health for all).
Lorien: There must be a glitch here because every time I play it the sorcerer (the second boss wave) and the two cave trolls (in the last level) all die instantly when you attack them for the first time. Anyone else see this?
Osgiliath: Way harder than levels 4-16 - that notice should really be changed.
If you are standing in the right place you can just barely see part of Minas Tirith shining in the distance - nice touch.
Continued . . .
Osgiliath Sapper Tips:
On Wave 4, they will only come from one direction at first (the rock-pile entrances at the ends of the bridges), so focus all fire in that direction. But after Andriel announces the second group, they will start to come from both directions. Then you should either cover both directions or start running, depending on how overwhelmed your group is.
On Wave 9, it's just sappers and they only come from the center of the arena, which means that if you stand in the hallway right next to one of the entrances to the bridge, all of the sappers will funnel into one stream on the bridge and you can aim in the same spot to kill all of them coming in single file. Just stand to one side of the entranceway with the pile of rocks to your right of left and shoot them as they come into view.
Because of her rapid fire attack with no reloading, running and gunning with Andriel seems like the best option when fleeing from a tail of sappers, but Farin's quick-revive ability with War Cry is more valuable. So instead of just running laps around the map and turning around to shoot the sappers, which entails significant risk and lets them catch up with you, just run laps and revive your companions with War Cry when you get to them. It's quicker and easier to execute than spinning around and aiming and it actually temporarily stops the pursuing sappers.
Farin is the best choice for completing the Osgiliath challenge mission. His explosive bolt can handle all melee enemies and War Cry, as shown above, can help you with the running technique. The only drawback to using him is that sorcerers in Wave 5 can still one-shot him and he has no way of shielding himself like Andriel. The only way for him to complete Wave 5 on singleplayer is to hide behind a wall, then suddenly pop out and shoot the sorcerers with charged shot. I've also noticed, interestingly, that explosive bolt can penetrate shields and walls - but be careful, because sorcerers also get splash damage through walls and you could actually be killed by one while standing in the hallway.
Eradan may be the best choice for Lothlorien. His multi-shot works well in the open environment where he can position himself at a distance to target almost all enemies with one shot. The skill is particularly useful for wiping out waves of sappers. During the last wave when sappers spam you from all directions, Evasion certainly helps slow down the chaos and makes the running/rolling tactic easier to execute. The bosses fall so easily that Farin's exploding bolt really isn't necessary.