Phantom is the first boss that you'll fight. He's one of the many recurring bosses in the game and you first encounter him in Mission 3. He is also encountered as a non-mandatory boss fight during Mission 4 and 7 (You can fight him if you desperately need the orbs). The final encounter is at Mission 8, though he can also be fought one more time when Nightmare engulfs Dante in M16 and puts him in an Underworld arena with a Shadow Phantom. Players usually reset at this segement due to:
Note: on DMD, Dante Deals 1/3 of Normal damage even in DT.
The idea is to keep the HB stun loop going, but the start up is different for both encounters. With Mission 3, the RNG is usually determined by how fast he ends his fireball pattern. For example, These are worst case scenario. You want to HB in DT as soon as possible and hope he doesn't perform fast fireball. Fast fireball pattern from phantom is the root of the problem.
At the beginning, the start up may looks like a JC but, that is the biggest misconception of this fight. At the same time, you can use it as a rhythm to get the critical hit loops timing right.
Once you get the inital hit then you have to maintain the loop. You have to be able to land another quick HB during phantom's stun animation then chase him. Make note of where dante could land on his back for the critical hit spot. This fight will go the same way as long as you execute it right.
Ideal Phantom I
It doesn't change much here because the idea is the same. What makes this different that you have to lure him into a spot where you are comfortable with. You also have an advantage with the air hike ability to not worry about landing on his back, but it's highly suggested to do the same idea for the consistency sake.
Dante damage is significantly reduced (refer to HP Value), which means it will take more HBs and such to kill. It's not necessary to aim for the perfect fight as DMD in nature is extremely polarizing difficulty.
Stinger Usage Example
It's good to check the Frequently Asked Questions (FAQ) if you have general questions regarding the bosses.