To unlock the Not So Mono trophy in Cities: Skylines, you will need to purchase and install the Mass Transit DLC.
The Monorail becomes available once you reach the Small City milestone at a population of 2,600 - 11,000 depending on which map you start with.
Once you have Monorails available, buy any of the two monorail stations (you can use any of the four different types available) and loop the monorail tracks around so that they join up. Create a new Monorail Line at one of the stations, add a stop at the next station and then return it to the original station to complete the line.
Repeat 9 more times to unlock the trophy. You will also unlock the trophy below when you reach 3 lines: