You Must have all Heart Pieces, Subtanks full, Armors, 4 blue upgrades, and full life when you enter the room. When you are in Sigma stage 1, go to the part where there is a big fall. Dash to the other top side and get an armor. Get at full energy and go down to where spike balls are. At the first one before it go down the hole and get out of the armor and slide down on the left wall. Go in a secret passage and get the upgrades.
What you do is get to the second level of sigma's stage and make sure Zero is still alive and you killed Vile by free will. Now when you get to the sub boss, switch to zero and kill it. It will land on you and Zero will die but you get the Z-Crescent.
It's weird, due to the lack of arm upgrade 1. Do the same as Z-crescent but don't get the arm upgrade.