Fair warning: I am completely and utterly warping everything in both universes to suit my needs. I do not own Pacific Rim or Katekyo Hitman Reborn!.
When Tsunayoshi Sawada was seven years old, his mother was killed in a Kaiju attack in Kyoto, and he was found by Herc Hansen while hiding several other children from the Kaiju. With a nonexistent father, Tsuna is taken in by Marshall Stacker Pentecost. In a random, out-of-blue, to-hell-with-it test, Tsuna shockingly proves that he is more than capable of fighting in a Jaeger, and becomes the youngest Jaeger pilot in history, alongside his partner Andres. The two fight Kaiju together for four years, until Andres is killed in the Drift while fighting a class III Kaiju.
Now, the breach is sealed, the people's memories of the Kaiju wiped, and Tsuna has returned home to Namimori with Hikari Kita, his partner since Andres' death, and their Jaeger, Frangipani, in an underground vault hidden from even the eyes of the coming world's greatest hitman, Reborn, who is coming to do two things: 1.) receive the greatest shock of his life (curse Iemitsu and his crappy reports), and 2.) train Tsuna to become Vongola Decimo.