SImply complete the monorail objectives as the description says. These are the pink triangle icons that are scattered around the outside ring of the map. You can usually see 2 or 3 at once on the map depending on how you're playing; more will appear as you defeat each one, or as you discover them as you tootle around the map. You'll need to complete them all, not just the number required to make ROXY vulnerable.
Most of the attacks require you to blast away at the station guard robots, and then once the required number have been defeated (you can check you progress in the tracker at the top left of the screen) the Station Master will appear for you to mow down. None of these are particularly troublesome but the onslaught gets worse and worse with each station you complete.
If you're having trouble run around the back of the station and have a moment to relax. Check up to make sure your health is not being whittled away by drones or the huge guns that run along the tracks overhead.
Once all the stations have been cleared, the achievement is yours.