Choose the "City Center" level from the mission select, then continue through a number of stages until you get to the one which has a downward-sloping zip-line with two aerial enemies shooting at you. You will notice that above is a vertical grapple point. Jump off the downward-sloping zip-line and grapple the bar above it, allowing you to discover the secret entrance.
The secret level itself is very straightforward. Once you obtain the item and exit the area, the achievement will pop.
Video guide: