Vehicle strategies are everywhere, but Retribution Paladins who would prefer to do something familiar should hop on a Salvaged Siege Engine, which plays the most like melee. The difference is that this isn't a DPS role, and steam pressure should be kept in reserve for Electroshock to interrupt Flame Vents and Steam Rush to create some distance when Flame Leviathan targets the player. It's still more about learning the fight and vehicle roles and less about any particular class.
Ignis the Furnace Master
This is a very good fight for Retribution Paladins, despite the need to move the boss around. This is because Ignis' most devastating attacks are easily avoidable by melee -- Scorch won't be a problem as long as players manage to keep behind the boss and Flame Jets won't interrupt anything as everything is instant cast. Even the geyser knockback (or up) won't make a difference because players staying close enough can keep hitting the boss.
The best thing a Retribution Paladin can do in this fight is actually during a non-DPS phase, when she's picked up an placed into the Slag Pot. Players specced for Divine Sacrifice should use it following a Divine Shield when placed in Ignis' belly, as well as ease burden on the healers by calling out immunity and even healing themselves. It's also a good time to remind players that they can (and probably should) use Fire Resistance Aura during this fight because all the talented benefit are granted through any aura.
This fight requires a lot of switches, which is actually better in practice than it is on paper for Retribution DPS. Retribution can pump a lot of burst DPS in the opening seconds of a switch, and players should always hit Crusader Strike first. Vengeance will likely be at full stacks, and Exorcism should be used while jockeying to get into melee range. Similarly, since Exorcism is low on the spell priority list, it's easy to reserve it for Wing Buffets which knock players out of melee range. Needless to say, step out of the fire -- staying out of the large circle on the ground should minimize this problem.
DPS on this fight is largely a matter of luck. If players get a Light or Gravity Bomb more than a few times, DPS will drop significantly. AddOns such as DeadlyBossMods allow players to check their range with a /range command, which should help remove the guesswork from knowing if the player's debuff will hurt anyone. Default range is at 10 yards and should be set to 15 to ensure that nobody else gets affected. Knowing exactly when to stop running away will also ensure players get back into DPS range much quicker.
As a melee class, Retribution Paladins are ideally assigned on the boss exclusively to optimize DPS to the heart when it pops out. Needless to say, always reserve Avenging Wrath for the exposed heart. Depending on the relative strength of your raid it may or may not be advisable to pop wings from the get go. Some raids get to the 25% threshold in under two minutes, in which case the players' DPS will be lower overall. If you bring Potions of Speed to raids, the last heart phase with Bloodlust is about the best time to use for optimal DPS.
The Assembly of Iron
This fight changes quite a bit depending on which boss your raid decides to do first, but whomever the raid chooses, the encounter is generally not very conducive to melee. The easiest fight and most common fight will be taking down the giant Steelbreaker first. Because Molgeim places Runes of Power underneath the bosses, the tank will move Steelbreaker around quite often. Ideally, the boss gets pulled out of the rune just far enough to remove the buff from the boss but still allowing melee to attack while on the rune but this won't always be the case. The most important advice to keep in mind here is to not pay attention to the DPS meters. DPS in this fight is artificially inflated by Runes of Power, so don't worry about it. Stay alive.
Players should be mindful of Art of War procs, easing healer burden by popping a Flash of Light between cooldowns. Keep up Sacred Shield because the damage from High Voltage (among other, non-persistent sources) is a nuisance. There really are no other tips for this fight other than paying close attention and know when to run away. Pursuit of Justice is awesome here because there's just a lot of running (away) involved.
This is a good fight for Retribution because it doesn't involve a lot of running around, and because Focused Eyebeams have a minimum range. Melee simply have to focus on Kologarn himself, with ranged DPS classes usually assigned to the arms. Retribution DPS is quite excellent on this fight because when positioned properly, Divine Storm and Consecration will hit all three targets. The arms are also close enough to switch to without having to move much or at all. Relish this opportunity and enjoy the fight as it's one of the few bosses in Ulduar where a Retribution Paladin can shine.