For this I used Ultimecia. You will real a lot of guides saying Emperor, Y'shtola, or Shanttoto. Emperor us really good because of his dashing circle attack that drops mines, but you really want Ultimecia.
To secret to her is her grounded Forward + Circle attack. You can charge it and unleash 3 projectiles. The projectiles do a ton of bravery damage to the summons.
I used Sephiroth and Ramza as my back ups, though I am not sure if who you use makes too much of a difference.
For EX skills I had Mighty Strikes and Rend Shield in my main and Provoke + Rend Shield on my back ups.
Using this team I was able to take out everyone but Odin.
The order of difficulty from easiest to hardest (in my opinion) goes: Alexander, Ramah, Odin, Ifrit, Levathin, Bahamut, Shiva, Shinryu
The hardest part of course is learning the summons attacks and knowing when to charge up Ultimecia's strike. It took me several tries to defeat Shinryu, but once I understood how to use Ultimecia I was able to beat Shiva, Ifrit, Bahamut, and Alexander all in one try. You mileage my very of difficulty but it is very doable.
For Odin all of his attacks were too fast I could not get any full charges off, so I switch to Emperor. The key to him is this Dashing + Circle. This attack places a group of mines where the Emperor is standing. To use it you need to dash up into the Summon's face and drop the mines. They do more damage than Ultimecia's attack and are faster. After I dropped the mines I would block Odin's bravery attacks and then dash up and repeat. The damage you do outweighs the damage Odin does.
I don't want to write a guide on each and every summons. There are plenty of those on youtube. I just wanted to put my thoughts on Ultimecia here because like I said at the beginning most guides you find say to use other people and I had so much trouble until I found the Ultimecia tactic.