After much frustration with Vossler U, I finally managed to master the fight.
Probably spent the better part of Sunday and Monday trying this fight, spending all stamina available on it. To date, I'd say this was the ultimate fight that gave me the most trouble, despite having pretty good XII synergy.
I'd get within 10-15% and then die which was super frustrating, I just couldn't muster enough DPS or keep the heals up on my tank or whatever. My first crack at this attempt was to use Advance on Lightning, and have her spam Crushing Blow. It worked well until the final phase when he one shotted her...I went to the drawing board and tried a few different strategies. I tried tanking, tauntilate, SG/SSII, healing, etc.
Ultimately, here's what I went with. Obviously this is dependent on your XII synergy and SBs I suppose. This set up was inspired by a No-Heal run I saw on YouTube.
This required: Crushing Blow, Sentinal's Grimoire, Boon
Took 4 S/L to get the optimal run, but it ended up working pretty well. Mastered with no deaths.
Lightning - Lifesiphon R3/ Drain Strike R3 / RM - Ace Striker
Sephiroth - Yukikaze R3/ Armor Break R4 - RM Dragoon's Determination
Tyro - Tempo Flurry R2 / Protectga - RM Dr. Mog's Teachings
Sazh - Full Break R2 / Power Breakdown R2 - RM Mako Might
Ashe - Dispel R3 / Ruinga R2 - RM Witch of Succession
RW - Galuf - Unyielding fist
XII gear used: Gungir, Platinum Dagger (4++), Loxley Bow, some 3++ Staff, Viking Coat.
Basic premise, Build up Lightning's SSB until you have three charges, cast Unyielding fist, and spam that SSB! If Lightning's health gets lower than others, switch to Drain Strike to make her the target for Vossler's phases.
Basically relied on Ashe/Sephiroth to do AOE damage to the guards while Lightning built up her gauge. Sazh's 1st turn should be applying power break down to Vossler, and Tyro casts Protectga.
Lightning was hitting for around 4k, Ashe 5k, Sephiroth 3.5k
Once guards are down, re-apply all mitigation. Begin hammering away at Vossler, and drop a SG just before he hits the first phase, then blast him with dispel.
Sephrioth switches to Armor Break, which hits for about 6k.
Once Ashe runs out of Ruinga, get her to defend until dispel is needed. (Remember, defend is active until you select the next command)
Sazh was mitigating and re-casting Boon when available.
Tyro was hitting with Tempo Flurry 1.1k each hit, and re-casting Protectga as needed.
Once Vossler activates mad mode and is dispelled for the first time, Lightning should use the RW for Unyielding Fist, and start spamming Crushing Blow. Each hit for Crushing Blow landed about 6.6k, with crits hitting for 9999.
This should take him down pretty quickly, just be sure to keep mitigation up as much as possible. i only had to use the RW once before he died. If I remember correctly, it took about 4 Crushing blows to take him down.
I know this is quite specific, but perhaps it might give you some ideas. Good luck!