You will unlock Dante Must Die Mode after you beat Very Hard mode. You will need to have fully upgraded all of your devil arms, devil trigger, guns, health, and styles to beat this. You should also have maxed out the number of vita stars, holy water and gold/yellow orbs that you can carry, and have a fairly decent amount of red orbs to buy more. It would also be smart to use Super Dante or Super Vergil. Enemies also have access to devil trigger, so kill them quickly before then can use it.
After beating this mode, you will Be rewarded with Super Sparda or Super Corrupt Vergil.
Dante Must Die Mode Stats:
Lesser demons and bosses health: 250%
Lesser demons and bosses damage: 250%