The LOTRO videos on this page show all of the major boss fights in the Grand Stair instance... even Igash on hardmode :)
It's probably the most popular instance in the Mines of Moria since it is the easiest. You can get through it in about 30 minutes, so it's good for grinding the Medallions of Moria to get your +10 radiance set.
The insidious cuff bracelet also drops from Igash on hardmode... which is still one of the best bracelets in the game.
Boss: Igash, Hardmode A lot of people have a hard time with this fight. The key is to control the archer adds. You're honestly better off having someone simply tank them so that they don't pelt the tank or the healer with arrows. Other than that you just need to tank and kite Igash til' he's dead.
Boss: Nardur the Shield Nardur is another easy fight. The hard part is getting to him in time for hardmode. I recommend standing with you backs to the gate so you don't get knocked off the edge. That aside, it's a quick burn.
Boss: Ilzkal the Pummeler Ilzkal the Pummeler is the first boss fight and is kind of a joke fight IMO. Just kill him quickly. When he puts the fear on you, use a pot quick or have the captain remove it. If you take too long he'll heal himself for each person with the fear on them.
Boss: Glothrok the Vile I'm not sure which is a more difficult fight in GS... Igash hard mode or Glothrok. Basically, start off attacking the boss. He'll then dismount. Kill the warg then the boss. He'll bring out three waves of warg adds. AOE and burn them down, then get back on the boss. Towards the end he does massive damage to the tank. If you aren't on top of the heals here your tank will go down for sure.
Boss: Gothghaash the Firecaller Gothghaash is a really easy fight. Just focus on him. Stay out of any fire he drops. When the fumaroles pop up, burn those down quickly as they heal him. Other than that it's no problem!
Boss: Dorozg the Beast Tamer and The Beast This is an interesting fight in the Grand Stair. Dorozg wakes up the troll, The Beast. It's not too complicated, you just need to stay out of the troll's aoe and have the tank hold aggro. Kill Dorozg and then the troll.
Hope you enjoyed the LOTRO videos for the Grand Stair... See you over in the other instances!