Elevator II is a skip done in Mission 12 to avoid getting on the elevator and fight Frosts.
General Info
Dante needs Air HikeStinger and Sky Star which is obtained from Trickster Lv2
It's possible to do it without DT boost by delaying Air Hike as much as possible. Although, it's not advised until the min-max grind. Conserving DT will only help killing first two Mephistos fast in Chrono Slicer room.
Vergil easiest method is to Air Stinger → Trick up → DT Stinger