The Monorail will unlock once you reached a population of 10,000.
Step 1: Select Transport. Buy any type off Monorail station. You can choose between Monorail Station ($15,000), Monorail Station with Road ($20,000), Monorail-Bus Hub ($32,000) and Metro-Monorail-Train Hub ($70,000).
Step 2: Connect the stations with Monorail Tracks. You don't need 3 stations for this achievement.
Step 3: Select Monorail Line. Press
on any station to Create a new line, go to another station and press
to add a stop. Go to the station where you started the line and press
to Complete the line.
Repeat Step 3 9 times and the achievement is yours.
After the 3rd time you will also unlock the triorail achievement.