What arcade game should I focus on to get 100,000 Nuka-Cade tickets?

The simplest and most consistent way to get tickets is to play the 'Bandit Roundup' game with a weapon with the Explosive Legendary Modifier, such as the Kiloton Rifle from Far Harbor. The AoE from the Explosive round will hit all the targets in both rows if you aim roughly in the center. Simply fire a round every time you see a target. You'll usually get 900-1000 tickets per game, so you'll need to play about 100 games to complete the achievement.

The reason for the variance is the fact that the targets generated are random. As they all have different point scores, you may get unlucky and have a game full of the lowest scoring targets, or one full of stars.

I had some luck cheating at the ball throw. Pick up the ball, hop onto the game and just move the ball up and down through the net. Once you get the right rhythm, you can rack up a pretty nice score.