Phantom Dust

This can be earned during the mission Panorama: Order: Search for Edgar. You can get this on a mission replay from the Simulator.

An easy strategy is to create a purpose-built deck intended to deal massive damage in an attempt to one-shot the boss. I used the following build to accomplish this quite easily:

1x Finisher - The skill you'll be using to kill the boss. DMG = DOUBLE your aura level
3x Bullet of Fire - To deal with the pesky egg bombs
2x Auto Shell - To protect you from the ricochet lasers
2x Laser Shell - To protect you from the bomb attack
1x Graceful Woods - To max your aura for the final attack
1x Level Amp - This skill will double your aura level as long as it's at or above 10
1x Level Boost - A quick 2 aura level boost
x19 Aura Particle

This deck results in a theoretical maximum aura level of 42 which would result in a possible 84 damage from a successful Finisher attack. Your goal with this deck is to build up an aura level of at least 15 so that the Finisher move does 30hp of damage which is Carcino's health level.

If you manage to beat Carcino without retrying you will also unlock:

Most of the guides describe arsenals with rare skills. However there is "cheap" way to beat the boss, with only two common items. Rock Shoot and Bullet of Fire. I found a lot of both in Junk and in the shop. Another two items I suggest is Healing Water if you make mistakes with the self destructing drones and Psycho Spear which is a little harder to come by but deals more damage than Rock Shoot.
3x Rock Shoot (RS)
2x Psycho Spear (PS)
3x Bullet of Fire (BF)
2x Healing Water
Rest is Aura

As soon as the battle starts pick up the orbs as fast as you can. If you don't provoke the boss it won't release self destruct drones until you are at your last 6 skills. Just build up as many Aura as you can and put one of the attacks on every free button. Overwrite with the same if you have to. Always leave one slot free (sacrifice healing if you must because it is extremely important to have high aura. The boss will shoot with its lower canon sometimes but it can be easily evaded either by hiding or running away. When the first bomb is released ether shoot it with BF or eat it and heal. Then step in front of the rest of the orbs (to avoid picking them up accidentally because you will die if you use them all) and spam PS then RS. It doesn't matter if the eye is open or not you have so much Aura it will hit most of the time.

The point of this strategy is taking advantage of the slow wind up phase ofthe boss. If you hit it quickly the majority of the battle happens in its slow phase so it eats all the attacks. It had around 10 HP after my first volley.

When the boss pulls up its belly back off as much you can and spam LT. As soon as it locks to the drones use BF and one shot them all. Run back to the boss and spam RS until it dies or releases another batch of drones. You will deal 4 damage mostly so it won't survive for long.