To unlock the No Fear, No Spleen trophy in The Grand Tour Game, you will need to win 50 races whilst racing as Hammond in Splitscreen mode. Any races in the normal episodes where you get to choose one of the show's characters won't count, unfortunately.
To make this easier/quicker, here are the best settings to use:
Local Splitscreen > Face Off
In the race settings, choose the following:
Car Class: Any
Track Selection: Choose
AI Vehicle Class: AI Off
Number of Races: 7
Car Selection: Rimac Concept One
Driver Selection: Hammond
Track Selection: Season 1 - Episode 1
Rabbit Dry Lake
Each race should take around 50 seconds to complete, and with 7 races chosen at the start, you'll minimise the loading time and event setup each time. Once you finish the 7 races, repeat the setup and grind away until you unlock the trophy.