This fight is a little bit harder than its molten core counterpart, with many new mechanics involved. Overall Ragnaros does hit a bit harder than most Firelands bosses so in that sense, a higher ilvl is required. The fight is divided into 3 phases and 2 intermission phases (similar to Lich King).
Phase 1 (100% - 70%):
Simply tank and spank the boss while dodging the Magma Traps. There are also a few knock backs that interrupt spell-casting. Stand right up close to the boss to completely avoid Sulfuras Smash. The boss hits quite hard and additionally there is also a tank debuff, which piles on even more damage. It is highly suggested to use some cds such as Vampiric Embrace when the damage becomes overwhelming. Basically the aim is to quickly DPS the boss into the first intermission phase before the tank debuff stacks becomes too high while also keeping up with the heals.
First Intermission Phase:
Just choose 1 side (preferably the longer side with more adds) of the hammer and SW:P all the adds (Sons of Flame). They will die before reaching the hammer. Mind Spike the furthest add to buy extra time before phase 2. This does mean that the side you didn't choose will have its adds reaching the hammer. So far I have not made any attempts to control both sides' adds at the same time so I am not sure if it's possible to have no adds reaching the hammer at all.
Phase 2 (70% - 40%):
Magma Traps and knock backs no longer occur. Kill molten seed adds as soon as they appear. Usually 1 SW:P is enough to kill it. Also move out of Engulfing Flames. Aside from that everything else is the same as phase 1. You may want to reset that tank debuff at one point during this phase by using Mindbender to tank the boss and move out of melee range.
Second Intermission Phase:
Same as the first Intermission phase, except now there are two extra large scions to deal with. Forget about dotting up the Sons of Flames and focus on the Scions. Vampiric Embrace is quite necessary here to cover the huge amount of damage resulting from leaving the Sons alive as well as damage from the Scions themselves.
Phase 3 (40% - 10%):
You must burn down as much as possible before the first meteor shows up. This is because having a meteor up will force you to kite and this really kills DPS, especially for a Shadow Priest. Therefore it is recommended to save DPS cooldowns and pots for this phase. With DPS cooldowns, this phase might just be the easiest phase. This is your last stand, so give it everything you've got. Good luck.
Drums of Rage:
This drum gives a bloodlust effect. Best used for phase 3, but can also be used for phase 1. Phase 1 may not seem like a good time to use this but the truth is that it is actually quite beneficial to use it in phase 1. Phase 1 is all about mana conservation while pushing the boss as quickly as possible into intermission phase. This is because phase 2 is really demanding on mana (from Flash Heals). So if phase 1 were to be dragged out, there is a high chance that mana will become a problem in phase 2. Of course as ilvl increases, this becomes less of a problem.