Usually I just go around and use Tidus, Rikku/Yuna and Auron. Tidus would be my main damage dealer, Rikku/Yuna are the healer (which is out depends per game) and Auron is mainly there to survive in case things go wrong. Though he also packs quite a punch
The start of the battle would be to play around with haste to get in between Seymour and Mortiorchis so that there Lance of Atophy => Full Life combo gets interrupted by at least 1 unit (which can then use a holy water). This would even go as far as simply casting haste on Mortiorchis (as he doesn't deal that much damage anyway).
Second of all once you've got him down to half health make sure to keep a shell (yes shell not protect) going on Auron, if you've been using him so now and then he should be able to survive Total Annihilation (unless you got really unlucky). As far as I know Seymour always uses Dispel the turn before Total Annihilation, so right after that cast shell on Auron and set him in defence mode. Usually I'll survive the Total Annihilation take 1 round to fix up my characters and get rid of Seymour before he can cast it a second time. Usually do have a Bahamuth with overdrive ready on standby, but apart from that I never really save up overdrives for this fight.
If you are planning on using a summon overdrive rush on him the second half of the fight (when seymour has lost half of his life) would also be the moment to do so.
On an other note Seymour is not immune to poison. So another strategy would be to both poison and silence him and remain on full defence duty. The poison will slowly kill him and the silence prevents him from casting dispel on you. This way you can keep up a full protective cast on your entire party. Only tried this once, but as he can't cast dispel I missed my early Annihilation warning and still got wiped out (as Auron wasn't in defence mode to survive the hit).
In Theory you could counter this by only using defence and letting poison do the work entirely, but I never tested this as it would just be boring
Summoning an Aeon when Seymour is about to use Cross-Cleave or Total Annihilation should be an obvious strategy, but it's still worth mentioning.
Can't say 100% sure as I've never tested this through. But the few times I did try to summon block Total Annihilation, Seymour just casted Banish before using his Total Annihilation thus effectively countering my summon block. As said can't say for sure though if this is programmed that way or just me being unlucky.
For those on a NSG challenge the best way to win this fight would be to use Rikku overdrive. If you've set over all 26 the al bhed primers from another save you should have gotten 99x Underdog's Secret from Rin on the airship. If you haven't done that you can get 30x wings to discovery from the chocobo race on Remeim Temple by finishing with 3 chests.
If you mix either one of these items with the lvl. 4 key sphere you can find on Mt. Gagazet you get the almighty "Trio of 9999" overdrive. Meaning every attack will now deal 9999 damage so in other words a 8 hit kill for our Seymour. Combine that with a good 8 hit overdrive (like lulu's using a weak spell) and he's gone before you know.