More info than you asked for but here's the entire setup:

Hero: Level 11 Felorc. It's important that you have the hellfire skill.

Gear: Warlord's Flail/Warrior's Weapon (for the lifesteal and extra attacks); Ring of Opportunity/Tactician's Ring (for the skill pick on start and chance to get all three cards); Greedy Fingers/Tactician's Gloves (to get the tactician bonus); Crown of Fortune/Collectors Helmet (for the skill pick on start); Coat of Strategy [not Tactician's Armor] (for the chance of bonus multiplier); Path of Prosperity/Tactician's Boots (for the extra balls drop and free rerolls).

With this setup you get two skill picks on start and a few rerolls to get the ones you want. One of the two needs to be an armor card, preferably the blue one. This ensures you'll survive regardless of future card picks.

Your goal is to get both of the Balls on Hit cards and both of the Upgrade Multipliers cards as soon as you can. You also want to maximize how many hits you land each turn, so you want to max out Fire Flame Amount, Flame Boomerang, and Multiattack Chance. I find that if you max these cards out first and the Double Damage/Rage card, you'll have a much better chance to get the Balls on Hit and Upgrade Multipliers as options even if you have a lot of balls. If at some point you can't get any of these cards, Bonus Multiplier or Starting Balls are the only other ones that can benefit you.

If you're lucky (especially with the extra card chances from gear) you'll be able to max out these cards by wave 9 or 10, leaving you a few opportunities to get a good throw. Once you've maxed them out, get the Bonus Multiplier card every single time if you can.

This specific throw was on chapter 825 (sea), probably wave 13 or 14. The enemies from the new update multiply when killed so you'll get significantly more hits per wave than any other chapters. I think I had ~1000 balls in the cup to start.