The task in this Secret Mission is to achieve a critical hit on the single Sin Scissors that spawns here. The ideal way to do this is to wait until the demon opens its shears in preparation for an attack, then, right as they are fully spread, strike them with Alastor. If timed correctly, the shears will be knocked aside: quickly have Dante step forward until he is touching the Sin Scissors, take aim with the Shotgun, and fire a single shot.
There are two signs of a successful critical hit: the first is that the Sin Scissors will immediately drop five Red Orbs at the start of its death animation, rather than only dropping Orbs at the end when it disappears. The second is that the Stylish Rank will immediately jump up to C (Cool!).
The Sin Scissors can also be knocked into critical state with the Shotgun itself, though this is a lot more likely to fail the mission than using Alastor.
What matters in this mission is that the Sin Scissors is killed in its critical state: the failure condition is if it takes damage while not in this state, so it is actually possible to kill it with more than one shotgun blast and still claim the reward.
Because the mission takes place under the cursed ocean, Dante's health is constantly drained, making repeat runs tricky. Dante cannot actually die just from being underwater, however: it will only drain his health down to the final "magic pixel." This does, however, mean any hit from the Sin Scissors will kill him. The best way to remedy this is to Taunt the Sin Scissors and use Devil Trigger to restore health.
Success will grant Dante a Blue Orb Fragment.