For the greatest probability that's strictly less than 100% (Fake Out/holding your opponent up in Sky Drop), using a double battle with significant cooperation between the players...
Suppose your opponent has a Hustle Togekiss holding Ring Target. You have a Cute Charm Skitty which Togekiss hits into to get itself attracted, and you hit Togekiss back with six Mud-Slaps from Skitty (this is why Iron Ball/Ring Target is needed) and a Nuzzle from one of its teammates. Togekiss's teammates include an Audino with Role Play and Entrainment, which it can use to copy Sand Veil from one of Skitty's teammates and pass that ability onto Skitty--as well as to another Skitty teammate after a switch, this time a Drowzee. Audino then gets itself KO'd from Skitty's and Drowzee's moves.
Eventually Togekiss's team gets down to 2 Pokemon, and on some turn, all of the following have to happen: Togekiss uses some move, its teammate sets Sandstorm, Skitty KOs the teammate, then Drowzee hits Togekiss with Confusion (Drowzee must be slow enough that this happens after Togekiss's turn, despite the paralysis) and picks up the move's eponymous side effect.
On the next turn, Togekiss attempts to use Focus Punch, and both Skitty and Drowzee attempt to use Assist. Both of them are holding Wide Lens, and their team's moves are carefully chosen to be the two copies of Assist, 21 damaging moves that all have 100% accuracy, and a single copy of Hyper Beam on something in the back. Because all of Togekiss's teammates have fainted, both Assists will be assured of aiming in its direction, instead of being diverted onto a teammate.
In order for Togekiss to successfully hit its move this turn, all of the following have to happen:
- It has to avoid hitting itself in confusion. 67% chance (USUM) or 50% chance (ORAS). Since USUM are the most recent games in which Assist exists, let's be charitable and use those mechanics. (There's a chance for confusion to wear off, but not until at least one turn has passed, which is why it's important to have that confusion only put into place last turn, and only after Togekiss has taken its turn.)
- It has to avoid being fully paralyzed. 75% chance.
- It has to avoid being immobilized by Attract. 50% chance.
- It has to pass its accuracy check. Focus Punch is normally 100%, but Togekiss being at -6 accuracy reduces that by 1/3, Hustle multiplies that by 4/5, and Sand Veil by another 4/5. This leaves just a 21% chance to hit. (Note that accuracy and evasion are combined into a single number before being applied, and that single number is still capped at +6/-6, so adding evasion on top of -6 accuracy won't help to reduce the accuracy even lower.)
- And the doozy: It has to avoid getting its focus broken. Focus Punch is a negative-priority move that waits to see what the opponent does, and if the Focus Punch user took damage from an attack earlier in the same turn, the move does nothing. Assist is a move that's similar to Metronome, but instead of considering the entire gamut of moves that exist in the game, it only chooses from a maximum of 20 moves: the ones that your teammates have, minus any moves on its hardcoded exclusion list. Assist is obviously on its own exclusion list to prevent an infinite loop, so two Assist users on the same team will only be able to choose from among 19 moves each. We already saw that by team construction, all those moves are 100% accurate attacks which can't help but hit (the Ring Target even eliminates cases of type immunity), with one exception. The only way to avoid breaking focus is if both Assists can manage to call up Hyper Beam, which normally has 90% accuracy but is increased to 99% thanks to both of them holding Wide Lens, and then it has to latch onto that 1% miss chance twice in a row. In all, the odds that Togekiss gets through this step all by itself are 1 in 3,610,000.
After factoring in all the other steps, the final odds of Togekiss failing to hit its move for some reason or another are 99.9999985457%, leaving less than a 1 in 68 million chance of success. Which is still more than 4 times as likely as winning the Powerball jackpot on any given ticket.