Taking seriously good care of them each generation.
I have a story simmilar.
Back when I owned my V1, I was taking so good of my Tamas, that I was always getting Mimitchis and Mametchis. I started to get annoyed. Then finally, at my 7th generation, I thought that I was going to get another Mimi-Mame. But, when I left my Tama underneath the neglectant care of my BFF while it was a teen for a few days.
But then during the time she took care of my Tama, she called me to inform that my Tama had turned into an adult. She described the character and I looked online for the Tama that matched her description.
IT WAS A TARAKOTCHI!
I was just so happy because my pattern was finally different.
Then after that generation when it was just under my care. I had gotten an Androtchi, and a Kutchipatchi. All different.
So you see, if you are really tired with getting the same character over and over, change the way you take care of your Tamagotchi in just 1 generation and then it brings you to a new pattern of Tamagotchis.
Don't try to kill it. If you're always keeping it fit, try to let it go fat the next generation! You'll get new characters!
Take my advice. It will most likely work!