Why bother with hard modes at all? Fortunately, that's answered for us - not only achievement points (which enlarge our, ahem, sense of virtual importance) but often extra loot, and completing certain hard modes unlocks Algalon the Observer, Ulduar's extra boss. So in a way the introduction of hard modes, ostensibly to ensure everyone can access content while still giving guilds a challenge, is contradictory; guilds who are unable to complete hard modes won't see all the content. I'm guessing this isn't an issue for some people, while others expect to see it during tier 9 at the very least, and yet more are a little peeved by it.
Hard modes aren't really defined anywhere in-game -- take a look at your Ulduar achievements tab to see a vast array of bewildering achievements, from the humorous (mumble feral druid mumble) to the bizarre. Fortunately, there's a bit of a clue as to which achievements are considered important by looking at the meta-achievement, Glory of the Ulduar Raider.
Let's take a look:
Flame Leviathan - Orbit-uary
This one's pretty self-explanatory: keep four towers up and defeat Flame Leviathan. Unlike some of the other hard modes, this totally changes the dynamics of the fight from something that's pretty laughable to a very complex encounter. You'll need your highest ilvl gear for this, and it's probably worth 'practicing' with fewer towers first to get a feel for how the fight's different from normal mode. Ignis - Stokin' the Furnace
Simply a time-based achievement, so as with other DPS races, ensure you're performing at your best and minimise the number of healers and tanks required. The problem with achievements like this is knowing when you've failed and controlling a wipe -- if it's very close and the boss has DoTs, he can die before you do. Get timers, get someone in charge of calling a wipe, and get good at dying fast! Razorscale - Iron Dwarf, Medium Rare
Kill 50 dwarves with Razorscale's breath (halitosis can be fatal!). Interestingly, unlike other 'kill N' achievements, this seems to be cumulative -- so you can keep dragging dwarves into her breath every time you fight her until everyone has the achievement. It's just a matter of co-ordinating tanks and adds to ensure they die to the breath. XT-002 - Heartbreaker
With this achievement recently changed, it's definitely doable now. The idea is to destroy XT-002's heart in one go when it spawns at 75%, requiring very good use of cooldowns, consumables etc to pump out maximum DPS during that period. As the boss has an enrage timer, high DPS is the overall theme, as well as coping with the usual encounter frills like Gravity Bomb, Tympanic Tantrum and Light Bomb. Iron Council - I Choose You, Steelbreaker
This is the first 'hard-mode' achievement that significantly changes the nature of the boss encounter. The Iron Council can be fought in multiple ways, depending on which order you decide to kill the dwarves. For the hard mode, it's Steelbreaker last; this is (unsurprisingly) the most difficult way round. Killing either Steelbreaker or Molgeim last drops the Archivum Data Disc which starts the quest to unlock Algalon, so even if you don't manage this achievement first time round, try Molgeim.
Different abilities stack up as the dwarves die, meaning overwhelming damage to the Steelbreaker tank by the time he's the only one left alive; unfortunately, raid deaths heal him, so it's a matter of zero casualties and sacrificing tanks (several guilds used voidwalker tanks for this, as their deaths didn't heal him, but apparently this has been fixed now). Practice until no raid member dies, as you really can't afford the heals. Kologarn - Disarmed
Kill both his arms within 10 seconds and ensure he dies from the arm deaths to get this achievement in the bag. This just involves co-ordinating DPS on the arms and body to ensure the arms die first, and ideally that he's under 30% when they die, so their deaths - each removing 15% of his health - finish him off. You can kill the arms multiple times and still get the achievement. Auriaya - Crazy Cat Lady
Auriaya's pounce-happy adds deal a stacking DoT to their tanks. Presuming you've got the pull down to manage the adds on normal mode, you just need to off-tank them to get the achievement -- offtanking for the entire fight may kill your tanks, so think creatively about how you can avoid the DoT getting too high. Hodir - I Could Say That This Cache Was Rare
Another time-based achievement, this one involves killing Hodir in 3 minutes. Thanks to the NPCs available during the fight, this becomes about maximising buffs and minimising DPS time lost to freezes etc. As with other speed kills, you also want to minimise healing, and so minimise the amount of raid damage taken from Biting Cold and Ice Shards. Thorim - Lose Your Illusion
This has two aspects to it - firstly clearing the gauntlet at speed in order to reach Thorim before 3 minutes are up, ensuring Sif is part of the fight; secondly, dealing with the extra damage from Sif's frost-based abilities. The basic fight really stays the same, but with extra stuff to avoid, and extra healing needed - healers will need to be very awake to cope with tank damage as well as the raid. Freya - Knock, Knock, Knock on Wood
Ah, it's Sarth+3 all over again. Sort of. Leaving three elders up and killing Freya changes the numbers side of the encounter, but the fight itself stays pretty similar. The elders' buffs increase the damage done by Freya and her allies, so this achievement is about having enough DPS to kill the waves of adds -- and Freya herself -- while also having enough healing to cope with the increased damage. Self-preservation and high stamina are very important, even to the point of equipping stamina trinkets and respeccing to ensure you minimise the chances of death to unlucky combinations of effects such as roots, sunbeam, Nature's Fury and exploding adds. Mimiron - Firefighter
This achievement is really fun to do, but you will soon get tired of fire. Hitting the 'Do not push this button' button enables hard mode, starting a ten minute self-destruct timer and increasing his health and damage. More importantly, the element of fire has been added to the fight, with Archimonde-like fires snaking around the room that need to be avoided and controlled, and extra fire-related encounter elements such as Frost Bomb and Flame Suppressant.
You still need to deal with all the usual Mimiron fun such as Plasma Blast, Shock Blast, Proximity Mines, Napalm Shell, Rocket Blast... as well as avoiding fire. Have fun.
(Mimiron, Freya, Thorim and Hodir are the four bosses which drop sigils to unlock Algalon, once you've defeated Iron Council and started the quest.) General Vezax - I Love The Smell Of Saronite In The Morning
This hardmode also changes the encounter, as you have to leave the saronite vapours alive rather than use their mana-restoring capability. It's all about mana management, and then when the Saronite Animus coalesces from the vapours, ensuring your healers have enough mana to keep the tank and raid alive long enough to finish it, and the boss, off. A combination of a DPS race and a very challenging mana-management fight for casters. Yogg-Saron - One Light In The Darkness
Another fun variant on a fight that mostly involves losing buffs and outside assistance. Again, you can practice with three or two Keepers alive before trying one, as the combination of losing (nearly) everything can be overwhelming. It's up to you which Keeper you have up - they each contribute different buffs and special abilities.
Depending on where you have trouble, you can choose to: increase healing received and gain Sanity Wells (Freya); increase movement speed and destabilize tentacles (Mimiron); increase total health and enable phase 3 adds to be killed (Thorim); or reduce damage taken and gain ice blocks to save near-deaths (Hodir).
If this isn't challenging enough for you, try it with zero Keepers - you could even try this to figure out which Keeper you most need to save your raid. Hard or Not-So-Hard?
Some of the achievements above are clearly less 'hard-mode' than just 'special-mode' or 'speed-mode'. However, each of them poses a challenge and grants a feeling of achievement.
One thing I've noticed doing several of the hard modes above is that they really help you understand the fight. There's a lot to take in at once in Ulduar, and often our knowledge of fights can be a little patchy when our specific role in them isn't too complicated. For example, as I've alluded to before, I wasn't around during initial Ulduar clearing -- so when I turned up to Mimiron, I was told 'avoid x and y, stay behind him in phase 2, assist Bob'. However, while learning Firefighter, I really got to grips with every last boss ability and danger involved in the fight. It's the same with Yogg-Saron.
Thanks to the implementation of Ulduar as a 10 and 25-man instance, the hard modes are also really accessible to 25-man guilds by having groups, especially raid leaders, try them out on 10-man first to figure out what goes on and how best to beat the encounter on 25-man. Often things are a little easier on 10-man, due to the nature of the adjustment down to a smaller group; some of the DPS fights may require tougher class composition than we're used to in 10-mans, though.
The only thing really to say is that it's a shame so few of the hard modes drastically change the form of the encounter, with several number-based buffs adjusting the difficulty of the fight through gear, rather than through skill. Hardmodes like Firefighter and Saronite are really good fun because it's not just the same old fight with a time limit, or with increased damage; let's hope we see more of these in future.