Classic alpine route. Spectacular climb with thousands of feet of exposure down either side of the ridge. We attempted the North Pillar but had to retreat off that due to running waterfalls. The Mittellegi was a very worthy consolation prize. Highly recommended.
You have to traverse the mountain to get up and down it. The best strategy is to take the train up to the stop at the Eismeer glacier and go out the tunnel there and rap to the glacier. Traverse the glacier and climb to the Mittellegi hut. Spend the night there. Climb the route to the summit. Take the South Ridge Route down traverse around the Monch to the Monch hut and spend the night there. The next day take the train down from the Jungfraujoch or hike down.
Light alpine rack. One 9mm rope. There are a lot of fixed ropes put there by the guides but not to be underestimated due to its length.