Setting up your load-out
For glyphs, you are absolutely going to want to equip the Glyph of Divine Protection. The most dangerous parts of this fight are going to be scorpion phase, when the whole raid is taking massive chunks of fire damage and the healers are struggling to get everyone up. Anything you can do to lessen that hit is going to assuredly put you in their good graces.
Slap on the Glyph of Focused Shield as well for an easy damage boost. While there will be moments when there are two enemies up (or three or more if your DPS are having issues burning down cats), they won't be enough to invalidate this option. The fight is definitely a DPS race against a soft enrage, and every bit you can offer to help, even in this age of neutered threat, will be a boon to the raid. Plus, it'll help establish a better threat lead in the crucial opening seconds while you wait for the 500% threat modifier to do its dirty work.
For consumables, make sure you're chugging the Elixir of the Master and Prismatic Elixir combo. The extra resistance will be incredible for scorpion phase.
Lastly, make sure one of your equipped trinkets is the Mirror of Broken Images. The clicky on that trinket is incredible, and you will need it for Flame Scythe.
Opening with a bang
The beginning of this fight sucks, because sitting along with you in melee are all those trigger-happy ranged DPSers who normally can be allowed to go past 130% of your threat before they pull, but instead (thanks to their stacking with the raid) they can only go up to 100%. And believe me, they will push it. You'll need to front-load as much threat as you can to leap ahead of them and establish early dominance.
I use my usual opening: cast Divine Plea, activate Inquisition, hard-cast Exorcism,, ,, and let fly Avenger's Shield. At this point, Staghelm should have skittered up to you, and you can break into your 939 stride. Moreover, you can consider prepotting a Golemblood Potion as well, if you need it.
Once you've got him in position, just hold tight, stick to the priority system, and push out max threat. After 30 seconds or so, you should be firmly ahead where neither man nor mage can reach you.
And that's when you can safely start panicking about Flame Scythe.
Don't panic! ... much
Flame Scythe can get scary later into the fight. But in this first scorpion phase, it's fairly tame. Also avoid the impulse to blow Divine Guardian right off the bat; coordinate with your raid lead when it will be most beneficial. And keep in mind that like other 3-minute raid cooldowns, Divine Guardian will only be available every other scorpion phase.
Personally, you want to be explicitly sure you're using both Divine Protection and Mirror of Broken Images for every scorpion phase, especially on the later Scythes, which always seem to be the most precarious. It would probably make most sense to save them for any Scythes that are not getting a raid cooldown, so your damage intake is less spikey from Scythe to Scythe.
Consider using Word of Glory proactively as a cooldown. If you're ahead on threat and are preparing to throw out a Shield of the Righteous, hold off for a few seconds and use it to mitigate the incoming Scythe instead. You can get some practice in for our active mitigation changes in 4.3!
Also, for the lulz, you can throw out Holy Radiance when stacked. Even if it's just a piddling amount, every little bit helps.
Leaping into the fray
After scorpion comes cat phase. This is the part of the fight where you get to exhale and recharge your batteries a little.
It's fairly simple to tank. Every so often, Staghelm will leap at a random healer/ranged DPSer and where he once stood, a Spirit of the Flame will appear. It will begin attacking you, so you'll want to do two things here.
The first is rotate around the spirit (please don't keyboard turn!) so that when Staghelm dashes back in, he won't be attacking your backside, assuming he jumped behind you. The other is to immediately switch to the Spirit of the Flame and burn it down. You do not want to stretch out the amount of time you have two enemies attacking you. If everyone switches, they should melt away with little resistance.
Rinse and repeat
You'll go through the phases again, scorpion and cat, which some additional flavor thrown in via the Searing Seeds during one scorpion phase and the Burning Orbs during one cat phase. These, thankfully, are largely ignorable by the tank. You won't get the Searing Seeds debuff, and the DPS usually handle the Burning Orbs.
If when the Burning Orbs appear they are nearby, you might consider moving slightly away from them, or at least putting a pocket of DPS between you and the closest Orb. The last thing you'll need is extra damage taken.
As you approach the kill, the fight will get more and more intense thanks to Staghelm's stacking Fury buff (i.e., the soft enrage). He'll be slashing and leaping harder than ever. Play smart with your cooldowns (both personal and raid), and you'll drop him in no time.
Staghelm is one of two Firelands bosses that drops tier tokens (the other, obviously, being Ragnaros). As such, pray hard for Conqueror tokens so you can snag your tier shoulders.
The Bracers of the Fiery Path also drop off Staghelm. Awesome wrist piece, definitely worth pining for.
The Light and How to Swing It tries to help paladins cope with the dark times brought by Cataclysm. Check out our suggestions for protection paladin addons.