Well, this seems to work for me occasionally:
When you're on the 7th round or higher, there may be a kind of pattern. It's a bit hard to explain but I'll try my best.
Say you're supposed to press B when a Nikatchi appears. When you see a Nikatchi for the first time, pretend that's number 1 in a cycle. The cycle should then go a bit like this:
1. Nikatchi
2. (another Tamagotchi)
3. (another Tamagotchi)
4. (another Tamagotchi)
5. (another Tamagotchi)
6. (another Tamagotchi)
Then after number 6 in the cycle the cycle should go back to number 1, which is Nikatchi. So you might even have to press B while number 6 in the cycle is appearing because once I pressed B and it beeped while one picture was appearing but the TV's flashes didn't stop until the next picture appeared!