From Sonic Retro
In Sonic Adventure 2, the Jet Engine is an upgrade to Doctor Eggman's walking mech. It enables the mech to hover short distances after jumping. It is necessary to complete the level it is located in: Lost Colony.
To get the upgrade, proceed past the first Point Marker, and you will come into a room that is in complete darkness. Navigate through it until you find a way to the upper level. The Jet Engine will be there waiting.