It's been a while since i've been on the Paladin forums but as my first max leveled job, I still frequently make use of my Paladin and enjoy the utility it provides me.
I have begun experimenting with killing NMs in Abyssea on pld/rdm. I am well aware that there are many job combinations that will do what i'm going to write about better, faster, and more effectively. But notwithstanding the eventually "Why not just level xxx and do it that way?", I will let you know what I have personally killed and how on pld/rdm.
The things that make pld/rdm great outside Abyssea help it in Abyssea as well. The complement of atmas, buffs, and temp items can turn a pld/rdm into a very effective soloer of NMs - mostly the ones used to make popsets for the big guys in Visions and Scars areas. I have not personally tried any NMs in Heroes but it would not surprise me to see it be possible on some of the 5th or even 4th echelon nms.
I have focused mostly on Scars areas since my shell is currently working on multiple level 85 Empryean Weapons and being able to come prepared with a pop saves a lot of time.
The other great thing about this is Paladin has a good chance of being able to proc red !!, which is the main allure for me. Being able to just solo pop sets on my own is a huge time saver and sometimes the additional prep rewards me with some of the drops from the main mob. Only the Scythe, Katana, and Great Katana WS can't be done by PLD.
Atma combination: Mounted Champion, Plaguebringer, Razed Ruins (or Gnarled Horn for higher double attack mobs
So far i've tried mobs in Misareaux, Vunkerl, La Theine, Konschtat, and Tahrongi.
Abyssea - Misareaux
Soloed kills - Funereal Apkallu, Manohra, Asanbosam, Cep-Kamuy, Athamas, Gukumatz, Ironclad Observer
Notes: For all mobs, full time Phalanx, Enlight, and Ice Spikes. Use appropriate barspells for status and element. Use attack food except for Asanbosam because he can dispel your food.
Asanbosam: Try to Shield Bash subsonics if possible, or remove it with a Catholican, Vicar, or Clerics' drink. The defense down is very hard to just deal with as it will increase his damage to 150-200 per hit even with Phalanx. If you are out of these and get Subsonic'd, use Sentinel. He also gains endispel for about 20 seconds after using Subsonics so reapply buffs as needed.
Manohra: Baraero will help cut damage from his TP moves.
Funereal: If you get a link or two on the pull, kill them if there is no competition. Otherwise they won't hit you for much and the regen from your atma should make their damage nearly negligible. The additional TP you get from shield blocks may actually help.
Athamas: Try to remove the slow similarly to Asanbosam - it is vicious.
Gukumatz: Good luck on the pull and/or the competition - if the pull is clean he's a pushover.
(Cep-Kamuy is much easier on blm because you can kite nuke him, but you can't do any red procs)
Gnawtooth Gary, Lord Varney, Chhrr Bati
Gnawtooth: His wild carrot sucks because it heals for so much. I typically swap out Plaguebringer and use Razed Ruins and Voracious Violet. He doesn't hit all that hard. Just that Wild Carrot can prolong the fight.
Lord Varney: Full time Baraero and bring echo drops incase of Silencega and stand with your back to the wall to avoid any unnecessary aggro. He doesn't hit as hard as some people say. This will take a while as he has a lot of HP.
Chhrr Bati: Use temp items to remove his Dark Wave bio. He isn't all that hard. Just make sure to fight him far enough away from the bombs so you don't magic aggro.
(failed) Quasimodo: I was able to get Quasimodo down to 10% and likely would have finished him off, but his Shock Spikes got me for 2k damage and killed me. I found out that as his HP goes down, his shock spikes get stronger. He only has them when he does his "sitting" move before he uses the Shadow Burst move. Use Holy Water to remove the curse and stick a Cure IV on yourself. If I do try him again I may save Rampart for when he is under 20% and be sure to watch for his sitting animation and turn asap. I don't know if Barthunder would help or not, but will probably try that as well.
Bakka: If you have an Ice Sachet you should equip it as it could proc on any of his ice spells. As pld/rdm you will not be able to stun his spells unless you use shield bash or flat blade. You must use a good -MDT/MDB set and barblizzard. Doing so will reduce Blizzaga IV to around 600 damage. An amnesia screen isn't a bad idea either. You may consider using a Fools drink for the last 25%. He doesn't hit hard at all. I used MC, RR, and Frozen Fetters atma.
Balaur: His primary danger is his breath damage. The first 50% is manageable, but the last 50% his breath attack can hit for over 1k damage, so it is important to keep your HP up. At the time I did not use breath damage down atma (actually used MC, RR, and Plaguebringer), but if you have them you should put one in place in Plaguebringers' spot.
Piasa, Mangy-Tailed Marvin, Lugarhoo, Baba Yaga, La Theine Liege (can probably solo all 3 Gigas for Briareus too but I have not tried yet)
Piasa: This fight is super easy as long as you stay buffed up. MC, RR, GH work best.
Mangy-Tailed Marvin: See Piasa.
Lugarhoo: When I killed him for the first time I was in a party of 3 and was level 83 (other was 90WHM and 90THF). If I had to fight him again I am convinced I would win no problem. I would consider using a Fanatics drink when he is under 15%, and a Champion's Drink because he will intimidate you fairly often.
Baba Yaga: See Piasa.
La Theine Liege: See Piasa, but ensure baraero is up and use your MDT/MDB set for Aeroga III if you can't stun it.
I don't envision much problem soloing the 3x Gigas for the Briareus pop. Would probably use MC, GH, RR for it if I try in the future.
Quetzalli: Keep barfire up. If you can determine what the red proc is precisely, save it until he is 20%. Then proc red and use some wings to knock him to 0% before benediction. Even if Benediction goes off, he's really no big trouble.
My main TP gear is Joyeuse, Dagda/Seignuir Shield, Incantor Stone, Creed Armet +2, Twilight Torque, Brutal Earring, Ethereal Earring, Creed Cuirass +1, Creed Gauntlets +2, Dark Ring w/ PDT-4%, Rajas, Atheling, Goading Belt, Creed Cuisses +1, Creed Sabatons +2.
My fast cast set adds Homam pants, Loquacious, and a fast cast Jeweled collar.
My healing set adds an Adaman Barbuta w/ 5% cure potency and hospitaler earring.
Shield skill set is Boxer's Mantle, shield torque, and Versa Mufflers w/ +5 shield skill
It is fun and as mentioned before, yes there are jobs that can do it faster and more efficiently. I think Paladin though is probably better equipped to get red !! and kill the mob than the rest of the jobs that can solo the above.
There are more on my list and if you have suggestions for mobs I should try let me know and i'll let you know success or failure.
Hope you enjoyed reading!