during my first play though i got it to work by summoning him with Yuna's Grand Summon Overdrive and giving him all my money, i had like 100,000 Gil left after having gotten his services (i had chosen the options to have him request 300,000 Gil, got him for about 190,000 Gil), the first time was over 100,000 but every time i gave him all my money while in overdrive he seemed to do it, when when i had like 20,000 to beat Sin (the battle where Sin approaches the airship and the battle ends in like 5 turns as his Overdrive increases)
in my second playthough, i chose the options so that Yojimbo was asking for 150,000 which made things easier but even with an overdrive and 50,000 he still isn't doing his ultimate attack
i ask as i have always had problems with Yunalesca, i can beat her first from with no Aeons and the second from i can beat her with either Shiva (due to her Overdrive only having her miss 1 turn, her Personal Attack Skill not making her loosing a turn and having Bizzara to heal herself) or my powered up Bahamut (who is dealing close to 20,000 damage from an overdrive and he's been taught Healing Spells), but her third from is what gets me every time, i normally have Yuna build up an Overdrive prior and save it for Yunalesca's final from
Best Answer
He has a hidden stat, call it affection if you want. How high it is when you get him is determined by how much you payed him to join you. Everytime you pay him in battle the stat goes up or down, depending on how much you give him. This stat greatly influences the odds of zanmato. I believe if the stat is too low it's not even possible for him to do zanmato, and when the stat is max and you give him more than a certain threshhold he has like 96% chance to do it.
I'm not sure about the exact numbers, but I will look it up now. I will edit this answer in a few minutes with the right numbers.
Edit: it turns out there is a lot more involved than I remembered. It's too much to post in here, but you can find it all in Azure_edge's guide under the chapter 'attack mathematics' (2.03).