For those still struggling with Aigion:
https://www.reddit.com/r/FFBraveExvius/comments/6otm3u/another_aigaion_guide_rikku_wol_cecil/
EDIT: Rikku needs to use her LB every 2 turns, not 3. This makes autoattacking with your filler units more important if Cecil isn't able to generate enough crystals with his 8 or 12 attacks. On the bright side, this lets your damage dealers regen some MP (if they have auto-refresh). Just remember Rikku LB takes priority over literally everything else.
This guide only requires Rikku, WoL and Cecil and allows for flexibility for those without hard-to-get units (Tilith, 5* chainers, etc.) and is based on /u/IceDragon247's comment. This guide will tackle the slow method (left arm > right arm > body). No TMR's are required besides Rikku's Pouch which is essential unless you're feeling lucky.
UNITS
Rikku
Rikku must be have her LB up every other turn. You have a 2 turn buffer to build it up and Cecil guarantees this 99% of the time. In emergency cases, get your damage dealers/MP battery to auto attack. After the first few turns she will not be doing anything besides rotate Synthesis > LB > NullAll regardless of whatever buffs are up. Gear her with Mog Wisdom, Override, and as much HP as you can (5.5k+). If you have the TMRs, equip LB building ones such as Ignorance or Kelsus' TMR.
WoL
WoL will eat every other punch from the left arm using Brave Presence. The first punch can hit anyone since reraise will always be up. On turns right after getting fisted, use Eccentrick from Rikku's Pouch. The LB buff lasts 5 turns but you do not want to risk something going wrong and not being able to build Rikku's LB. If you are using a mage or Fry, use his SPR break right after Eccentrick. Rotation will be Eccentrick > Brave Presence > Free Turn > Brave Presence. Gear him with Rikku's Pouch and maximum defenses. Give him dual wield if you have a spare one and reach 6.5k HP. Lucky Bangles and Assassin's Vest can be equipped as well (fisting is NOT dodgeable).
Cecil
Cecil is crucial to the team because he makes sure Rikku's LB is always up. With Second Knife and Twin Spear, he auto attacks 4 times. When paired up with Eccentrick, Rikku will almost always have her LB up after one turn. Even if you are extremely unlucky, you have a leeway of two turns to build it up. If Rikku's LB gauge is full, Cecil can use his LB to help your damage dealers kill Aigaion faster, help heal using Curaja, or use Bushido Freedom when necessary. REMEMBER TO TARGET THE BODY WITH YOUR AUTOATTACKS. Gear him with Second Knife, Twin Spear, Bushido Freedom, and maximum defenses. You can equip Cecil or WoL with Black Belt to help with LB crystals but it's quite overkill unless you're lacking Rikku's Pouch. Enhance Cecil's abilities if you have the crysts.
Healer
Tilith is the ideal healer as Cecil and WoL will be taking some big hits. Not so necessary because you can let them die on some turns if they have reraise on them. Prism Heal is great for MP sustain but you can just use MP recovery items with the other two party members (or bring an MP battery). Others have said DC Refia and Ysh are sufficient. I'd use Ysh for first turn defensive buffs and she's good for those without DC. Gear your healer for maximum MP/MP regen and SPR/HP. Since everyone is calling me out for saying Tilith, let me make it clear that with > 5.5k HP on all your units and with Rikku LB up every other turn, you will find that you will (almost) never require require a heal more than 4000 HP which Refia and Ysh should be able to do with even the most basic equipment. You can stack SPR instead of HP as well to further strengthen your heals since the two tanks are more than likely to take the hits if your healer is targeted.
Last Two Slots
You can either go with an MP Battery and damage dealer or two chainers for the last two slots. The former is much safer but the latter will be much faster. Just make sure that they have sufficient HP to survive after being reraised and hit without defensive buffs up. I found 5.5k to be a safe number. /u/Foxheart2's suggestion of using Emperor with Ling (or any other MP battery) is probably the fastest route especially since WoL will have some free turns to break SPR. Rem can also be used as a damage dealer and Bartz or Ilias can be used as mana batteries. If you plan to use two chainers, let them use MP items on your other party members. This takes priority over them attacking. Innate MP regen is preferred. You can gear them with as high ATK as you want. Remember that building Rikku's LB is priority so auto attack if Cecil isn't able to fill the gauge.
TEAM SET-UP
*Rikku: Override, Moogle Crown, Tabby Suit, 2x Muscle Belt, Mog Wisdom, 3x HP +10% *WoL: Gigantaxe, Hero Shield, Grand Helm, Assassin's Vest, Rikku's Pouch, Bangles, HP +15%, 3x HP +10% *Cecil: Second Knife, Twin Spear, Dragon Helm, Dragon Mail, Germinas Boots, Muscle Belt, Bushido Freedom, 3x HP +10% *Tilith: Cat Ear Hood, Fina's Clothes, Rain's Insignia, Vitality Apparatus, Mog Rise, HP +15%, MP +15%, MP +20% *Aileen: Genji Blade, Artisan, Black Cowl, Demon Mail, 2x Bracer, Dual Wield, 2x Quick Assault, Blade Mastery *Friend Aileen: Geared for max damage, preferably with Machine Killer
As you can see, only Aileen has (non-free) TMR's. Tilith is not essential as this strategy ensures +50% defensive buffs at all times along with cover from two tanks so healing from DC Refia or Ysh should be enough. If you do get unlucky, the free turns from Cecil and WoL will let you raise your units anyway.
STRATEGY
The first few turns are crucial. Once you get into the rhythm, it gets pretty easy.
TURN 1
Rikku: Synthesis
WoL: Eccentrick
Cecil: AA body for crystals
Healer: Buffs
Others: Help with buffs or attack body for crystals
No units have reraise. One filler unit is dead.
TURN 2
Rikku: LB
WoL: Free Turn (SPR break, Raise filler unit, or AA for crystals)
Cecil: AA body for crystals (LB/Curaja/Bushido as neeeded)
Healer: Heal
Others: Revive dead with Phoenix Down. DO THIS BEFORE RIKKU LB.
All units will have reraise after turn. Aigaion will kill your filler unit and s/he will reraise.
TURN 3
Rikku: NullAll
WoL: Brave Presence
Cecil: AA body for crystals
Healer: Heal
Others: AA body for crystals or Damage, MP refresh if LB is full
Aigaion will kill WoL and he reraises.
TURN 4
Rikku: LB
WoL: Eccentrick
Cecil: AA body for crystals (LB/Curaja/Bushido if LB full)
Healer: Heal
Others: Damage, MP refresh
All units will have reraise after turn. Aigaion will kill your filler unit and s/he reraises.
TURN 5
Rikku: Synthesis
WoL: Brave Presence
Cecil: AA body for crystals AFTER RIKKU LB
Healer: Heal
Others: Damage, MP refresh
Aigaion will kill WoL and he reraises.
Cycle After Turn 5
Rikku: NullAll > LB > Synthesis > LB
WoL: Free Turn > Brave Presence (get reraised) > Eccentrick > Brave Presence (get reraised)
Cecil: AA body for crystals or free turn if Rikku LB gauge is full
Healer: Heal
Others: Feed MP to team/Do damage
After Left Arm Is Killed 10x
Once the left arm is dead, you will find it much easier to survive. All units will do the same rotation except for WoL who will get another free turn instead of using Brave Presence. Use these turns to top up your MP for all your party members. You can deviate from the rotation if you want but I tend not to just so that I can keep the rhythm. After killing the right arm twice, you'll want to go back to the rotation because he uses genocide beam twice each turn and you NEED NullAll and Rikku's LB up at all times to survive.
After Right Arm Is Killed 3x
Repeat the rotation until right before you hit the 70% threshold. Make sure your entire team has reraise and then cross the threshold. Your whole team should die. On the turn after reraising, use Cecil's LB to boost your defenses and attack with your two filler units to build up Rikku's LB again. He will use World Destroyer every 5 turns (NOTE DOWN TURNS ON PAPER). Just repeat the rotation from before until you get close to the 50% threshold. You must cross the threshold 2 turns before the end of the 5 turn count to give yourself time to build Rikku's LB again. Delaying crossing the threshold will allow you to build up Cecil's LB as well. Do the same with the 30% threshold. Win.
. I'm going to try switching things up today, might bring WoL back in.
