Abilities:

• Fel Fireball - Inflicts 15,113 to 15,887 (25-Players: 24,375 to 25,625) Fire damage and an additional 5,850 to 6,150 (25-Players: 9,263 to 9,737) Fire damage every 1 second for 5 seconds. Interruptable, magic dispellable.
• Fel Lightning - Inflicts 7,863 to 9,137 (25-Players: 9,713 to 11,287) Fire damage to a random target and jumps to other players nearby, affecting up to 3 (25-Players: 5) targets.
• Incinerate Flesh - Absorbs the next 30,000 (25-Players: 60,000) healing done to the target and reduces damage done by 50%. If the spell is not removed by healing, it will cause Burning Inferno. Lasts 12 seconds or until the spell absorbs its healing limit.
• Burning Inferno - Inflicts 2,438 to 2,562 (25-Players: 3,900 to 4,100) Fire damage every 1 second for 5 seconds to all friendly targets. Cast by the target of Incinerate Flesh if the latter is not removed before its duration expires. Incinerate Flesh is removed after absorbing 30,000 (25-Players: 60,000) healing.
• Legion Flame - Inflicts 2,925 to 3,075 (25-Players: 4,388 to 4,612) Fire damage every 1 second for 6 seconds. The target also spawns a Legion Flame every 1 second. Each Legion Flame inflicts another 2,925 to 3,075 (25-Players: 4,338 to 4,612) Fire damage every 1 second and lasts for 60 seconds.
• Infernal Eruption - Summons an Infernal Volcano, which shoots 3 Felflame Infernals at players over 15 seconds. Every time an Infernal lands, it causes Infernal Eruption, inflicting 9,263 to 9,737 Fire damage to targets in a 10 yard radius.
• Nether Portal - Summons a Nether Portal and inflicts 6,825 to 7,175 (25-Players: 9,263 to 9,737) Shadow damage to targets in a 10 yard radius of the portal. The Portal spawns a Mistress of Pain.
• Nether Power - Increases magic damage done by 20% per application. Jaraxxus will buff himself with 5 (25-Players: 10) stacks.

Felflame Infernos

• Fel Streak:  The Felflame Infernal charges a target and inflicts 4388 to 4612 (25-Players: 6,338 to 6,662) Fire damage and triggering a Fel Inferno in the area.
• Fel Inferno: Inflicts 2,500 (25-Players: 3,500) Fire damage every 1 second for 6 seconds to targets within 15 yards.
  

Mistress of Pain

• Shivan Slash: Inflicts 50% (25-Players: 75%) weapon damage and ignoring armor.
• Spinning Pain Spike: Leaps to a random player and Inflicts high physical damage based on the target's maximum health.
  

The Fight:

Tank him in the center while the raid spreads out 360 all around him.   Try to maintain at least a 10 yard distance from each other and spread out your healers accordingly.   Melee will have to make due.   Use Fire Resist Totems/Auras to help a bit.

Otherwise this fight is fairly managable, it only looks scary cause of a lot of abilities happening, but once you see it once, you'll get a good idea on how to beat it.

Incinerate Flesh is the first major debuff you should be aware of.   You have to heal bomb the person that has it to cleanse it off, otherwise the raid will take additional fire damage.   Not a raid wiper, but will stress your healers out more.     You can cloak / bubble / block /etc out of this debuff.

Legion Flame is a green fireball that flies at you causing you to drop puddles of flame every second for 6 seconds, so 6 fires.    You want to move to the back wall as quickly as you can, or at least away from the raid.    Yes, it leaves a trail of fire, but if you move fast enough, there'll be gaps, easy for otherswalk around them.    If you don't move, that means you start dropping fires one on top of another.    Though that gives you more room, that sort of creates one "big" fire patch that'll become very lethal and one shot you if you happen to touch it (well 6 quick shots).

Fel Fireball is an incinerate napalm type attack.  It is interruptable.    Otherwise, still healable and magic dispellable if you miss that.

Fel Lightning is a chain lightning attack that chains through 5 of you.   Targets melee so they'll have to eat it.   Ranged should be spread out to avoid chaining.

Every 60 seconds, he will summon adds.   There'll be 2 types and he'll alternate their order.  They are to be OT'd and killed by ranged.  You can use 1 OT, and they have low health so should go down fast.

Also around this time he'll do Nether Power on himself, 10 stacks.  You are to dispel / purge / spellsteal (it works) off of him or his attacks like Fel Fireball becomes lethal.    You may have to do it multiple times if you don't get the 10 off right away.

As for adds type one is the Mistress of Pain, she whirlwinds (shivan slash), so melee stay out.   Tank her way from people.    She will randomly leap towards someone, heal that person or he's dead.   Something akin to KT's Frost Blast, it will eventually deal damage equal to their max hp, so give them something.    OT has to pick it back up right after.   

Type two is the infernos.   A volcano will spawn (think Supremus) and 3 Infernos will pop up (slight delay inbetween each).   Don't be near there, they'll do 10K damage upon landing.   OT just pick them up and range burn down again.    They aoe around them with Fel Inferno and randomly Fel Streak others.   

That's about it for the fight.    Tank and spank, spread out, avoid damage and fires, ranged kill adds, heal bomb Incinerate Flesh, move the fuck away if you have Legion Flame.     Easy enough boss.

Hard Mode:

• Fel Fireball - Inflicts 18,038 to 18,962 (25-Players: 34,125 to 35,875) Fire damage and an additional 7,800 to 8,200 (25-Players: 10,725 to 11,275) Fire damage every 1 second for 5 seconds. Interruptable, magic dispellable.
• Fel Lightning - Inflicts 9,713 to 11,287 (25-Players: 11,700 to 12,300) Fire damage to a random target and jumps to other players nearby, affecting up to 3 (25-Players: 5) targets.
• Incinerate Flesh - Absorbs the next 40,000 (25-Players: 85,000) healing done to the target and reduces damage done by 50%. If the spell is not removed by healing, it will cause Burning Inferno. Lasts 12 seconds or until the spell absorbs its healing limit.
• Burning Inferno - Inflicts 2,438 to 2,562 (25-Players: 7,800 to 8,200) Fire damage every 1 second for 5 seconds to all friendly targets. Cast by the target of Incinerate Flesh if the latter is not removed before its duration expires. Incinerate Flesh is removed after absorbing 40,000 (25-Players: 85,000) healing.
• Legion Flame - Inflicts 3,900 to 4,100 (25-Players: 6,338 to 6,662) Fire damage every 1 second for 6 seconds. The target also spawns a Legion Flame every 1 second. Each Legion Flame inflicts another 3,900 to 4,100 (25-Players: 6,338 to 6,662) Fire damage every 1 second and lasts for 60 seconds.
• Nether Portal - Summons a Nether Portal and inflicts 8,288 to 8,712 (25-Players: 10,725 to 11,275) Shadow damage to targets in a 10 yard radius of the portal. The Portal spawns a Mistress of Pain.

Felflame Infernos:

• Fel Streak:  The Felflame Infernal charges a target and inflicts 6,338 to 6,662 (25-Players: 11,700 to 12,300) Fire damage and triggering a Fel Inferno in the area.
• Fel Inferno: Inflicts 3,500 (25-Players: 5,000) Fire damage every 1 second for 6 seconds to targets within 15 yards.
  

Mistress of Pain:

• Mistress' Kiss:  Next spell with a cast time interrupts that school for 8 sec and causes 8288 to 8712 (25-Players: 13,650 to 14350) Shadow damage.

Well besides stuff hitting harder, so more emphasis on spreading out, kicking fireballs, and heal bombing the Incinerate Flesh to not fail and trigger Burning Inferno...   

The Nether Portals and Fel Volcanos are targettable mobs now that must be killed.    They will continually spawn their Mistress of Pain and Fel Inferno until they are.

Mistress' Kiss:  This should only occur when the Mistress of Pain is up, a random debuff that lasts for 15 seconds.   It will interrupt you.   Best bet, as long as your health isn't low and someone can heal you, is to probably cast a different school of magic to take the interrupt there.   Like Fire mages casting Frost, Shadow Priests popping a heal off, or something, whatever you like, or the school you hate.    Then you'd be able to continue on your task.   Holy Pallies are screwed though, could just take the interrupt for 8 sec, or be silenced for 15 sec, maybe limited to holy shocking.

Otherwise, same basic fight, if you got past the Beasts, this should be easy enough.

Achievements:

Three Sixty Pain Spike:  Defeat Lord Jaraxxus while at least two Mistresses of Pain are alive in 10/25-player mode.

Sounds like it's fairly simple.   Have the OT keep them around.   Range ignore her.   Heal through extra damage.   Though, not sure if 2nd OT needed if they both leap away to kill someone.

Videos:

10 Man:

25 Man (w/ Narration):