Mirmulnir is the first dragon you fight in Skyrim, and you probably badly want to make sure it isn’t the last. Dragons, however, are fearsome creatures- tougher even than giants, who only need to hit you once to kill you at this point. Fortunately, you have Irileth and several guards assisting you, but it’s still remarkably easy to get yourself killed in this fight with a single wrong step- usually right into a gout of flaming breath.
The first thing is to remember what you learned from the Draugr Overlord- when you fight at range, get distance immediately, killing whatever can wait until you’re at the right range. When you fight in melee, crowd in there quickly. And don’t forget to abuse your item menu.
There are a few other big points here. Mirmulnir probably won’t have to hit you more than a couple or three times to kill you off- so the first goal is not to get hit. As the dragon begins with a randomized set of strafing runs and hovering blasts via its flaming breath, your best bet here is to stay away from the guards and Irileth. Standing near them just gives the area-of-effect attacks a chance to kill all of you at the same time. Irileth is plenty tough, and the guards, sadly, don’t really matter. Make sure you’re far enough away from Irileth that the dragon will often be between her and you, and keep an eye on what it’s doing as you pepper it with arrows or spells. Splitting up means it will only belch flame at you occasionally, and if you’re farther off from the guards, then you have plenty of time to see the fireball coming and juke aside.
When Mirmulnir lands, ranged characters will just be happy. The bow can be used from well outside of the range of the dragon’s conical breath blast, and spellcasters can stay at the extreme end of range and move off to one side- remember, clustering up is begging to get coned to death. Melee-centered players face a small conundrum- do you attack from a range with probably your far weaker attack option? This can work, but it’s slow and tedious- and the dragon might finish with the guards and come after you, though Irileth’s huge durability does dissuade it somewhat. The other option is close combat- which seems likely to be suicide. Fortunately, for all its power, Mirmulnir can only face one direction at a time. If you come in from an oblique angle and/or circle around, you can attack the dragon from the side or behind at melee range with pretty certain safety. This also helps by letting the guards draw more attention, making it unlikely Mirmulnir will turn to strike at you before you have the chance to sink a couple of power attacks into its flank.
Again, this is a fight that is as much about tactical reaction as it is about power, so use your thinker and keep yourself untoasted.
