The parachute unlocks after all of Leonardos’s war machines have been destroyed. Meet up with him at the usual meeting place (the L icon), and you’ll have access to them. Once you have the parachute, climb to the top of Castel Sant’ Angelo (the top of the flagpole with a red flag) and jump off. This location is at the top of the map indicated by a circular shape. It is within a restricted area. The easiest way to get there is to wait until playing Sequence 8 Memory 2: "An Apple a Day". This mission is after a lengthy cutscene where a female is moaning and crying in a window. Look up and you'll see the flagpole you must climb. Get to the top of it and jump by pressing then press to open the parachute moments after jumping. If you die during this mission, you will spawn at the checkpoint near the window.
You may purchase parachutes by going to a tailor. To check if you have parachutes, press and select Inventory > Supplies > Parachutes. They cost 170 florins each.
Note: Sometimes the achievement won't trigger if you activate the parachute instantly after jumping. You should wait a moment before using it.