Although an easy fight, Auriaya requires some switching. Similar to the tips with Razorscale, opening with a Crusader Strike on the adds is a good way to keep up consistent, if bursty, DPS. There's a lot of shadow damage going around during this fight as well as physical, so Devotion Aura and Shadow Resistance Aura are both good choices here. The Seeping Feral Essence left behind by a Feral Defender is a really painful void zone that can kill low-health raid members feared through it, so shadow resistance helps (Priests can provide the same buff). It's a fairly simple encounter, and some form of fear break -- such as a PvP trinket -- can help, but isn't necessary.
This wonderful mechagnome and his inventions has got to be my favorite encounter in all of Ulduar. It wasn't a melee friendly fight, but Patch 3.1.3 is changing that, with most of the nerfs to Mimiron directly benefiting melee classes. Retribution Paladins shouldn't expect to do great DPS here, particularly in the first phase against Leviathan MKII. Because melee have to move away every time there's a Shock Blast, DPS can drop significantly. Camera should be zoomed out and maybe even panned at a bird's eye view in order to better see the Proximity Mines, and a route should be planned ahead before Shock Blast is cast.
Pop Avenging Wrath from the get go. As the Leviathan MKII will cast Shock Blast about 20 seconds into the fight, wings will fade just as players need to run out. This should also ensure that the spell will be available for Phase 2, which some raids have difficulty with. Raids progressing through Mimiron will sometimes use Bloodlust to get through the tedious part of the fight as quickly as possible, and Avenging Wrath should always be used along with Bloodlust for optimal DPS. Retribution Paladins, needless to say, should attack the VX-001 (Anti-personnel Assault Cannon) from behind, which should ensure that they'll never get hit by the P3Wx2 Laser Barrage. The spinning up phase is more than enough time for melee to reposition, and players can simply go through the boss to make matters simple. There's a lot of fire damage through phases one and two, so Fire Resistance Aura is a good aura choice. Patch 3.1.3 nerfed Rocket Strike so that it's less likely to target melee, which should help a lot considering seeing the crosshairs on the ground is difficult through Consecration, Desecration, and/or Death and Decay. Turn on Projected Textures in the video options to see ground effects.
Phase 3, when Mimiron flies up in the Aerial Command Unit, is where Retribution Paladins can do well. Melee classes are usually the ones assigned to pick up the Magnetic Core, and Paladins are a good choice because we can dispel Magnetic Field or use Hand of Freedom. It's possible to miss with the Magnetic Core, so placing it directly under the Aerial Command Unit is key. A bird's eye view can help with this, but it is much easier with a Hunter in the raid. Hunter pets can attack the Aerial Command Unit from the ground, making it easy to see at a glance where the Magnetic Core can be placed. Retribution Paladins should use Avenging Wrath when the boss is grounded as it takes more damage in that state.
The final phase, when all three combine to form V-07-TR-0N, is simply a matter of paying attention. Again, the Mimiron encounter was nerfed greatly here as the Leviathan MKII component will be stunned for the duration of the Laser Barrage. This removes the problem of repositioning, making it less likely to get hit by Proximity Mines. Use Divine Shield and Divine Sacrifice to soak up one Shock Blast and marginally reduce raid damage. Use of Divine Plea through every cooldown, and between each phase in particular, should ensure that Retribution Paladins never run out of mana through this fight.
Don't waste any effort DPSing Freya through Phase 1, that should be said before anything. Retribution Paladins can do reasonably well through this fight because of the adds. Well placed Consecrations and well-timed Divine Storms can pump our DPS considerably. Care must be taken not to be near too many dying Detonating Lashers at once. Taking one or two hits from a detonation is survivable but can be completely avoided. There's simply a lot of switching during this fight, and the idea is to down the adds as quickly as possible. Phase 1 where adds spawn is the only difficult part of this fight, and the raid must get there by any means necessary. There's quite a bit of movement throughout Phase 1, but it isn't nearly as detrimental to Retribution DPS because adds will be everywhere and Divine Storm keeps us productive. The only thing that curtails DPS here would be the Nature's Fury debuff, but Divine Shield can take care of that.
The Thorim encounter is pretty much all about trash and managing target switches and DPS priorities. Once the initial Jormungar Wyrm and humanoids have been slain, the encounter begins. Retribution Paladins assigned to the arena portion should probably focus on the Dark Rune Evokers, although it depends on how your raid handles the encounter. Evokers are key to the fight and should be killed first, but what makes it difficult is sorting them through the mess. A target macro comes in handy here, particularly when paired with a marking script for players with raid assist.
The mobs can be stunned, interrupted, or otherwise cc'd, and Retribution Paladins shouldn't hesitate to do so in order to minimize raid damage and prevent healing. The faster Evokers are killed, the easier the arena portion becomes. Staying in the middle of the ring minimizes getting hit by Stormhammer, as well as allows the best use of Consecration and Divine Storm. As with AOE situations, both spells have higher priority than either Crusader Strike or Judgements. Retribution Paladins assigned to the hallway simply must do their thing and avoid any player afflicted with Rune Detonation. Thorim himself is an easier fight than the gauntlet and is only technically demanding for tanks.