All credit goes to Poltergeise over at TrueTrophies and Omegamustard at PlaystationTrophies
respectively for this solution.
When you get into the game, be sure to load into litter box mode and punch in the following seed number:
-1957262312
Load up the first house and the very first event will be a mouse every time, so farming mice should take no time at all and the achievement will be yours!