Say my opponent and I each have 1 prize card left, then I use an attack like Pumpkaboo's "Reckless Charge" that KO's my opponent's Active Pokemon but also KO's Pumpkaboo due to "Reckless Charge's" recoil effect. However, my opponent has only one benched Pokemon with 20HP left, while I only have Iron Valiant ex on my bench. Does our game go to a tiebreaker since we both have a Pokemon on the bench, or will I win the game since Iron Valiant ex would be promoted as Active and then "Tachyon Bits" will be activated resulting in the KO of my opponent's last Pokemon?

All effects have to finish resolving before the winner is determined, so you could activate Tachyon Bits to KO the opponent's last Pokemon. You would win the game as you have achieved two win conditions but your opponent has only achieved one.

Relevant cards

SV4_77

SV4_89