Here's the guide for Devil May Cry HD that helps you out with Blue Orb pieces and Secret Missions, as both are tied in ways. Once again, read ahead at your own risk, as the below may contain some spoilers.
Strategy for Shadows:
The Shotgun or Ebony & Ivory are most effective for exposing the Shadow's core. Nightmare B is not recommended against Shadows, as it drains DT energy. Ifrit is also useful against Shadows; especially if you plan to deal a great deal of damage quickly, or you are in a confined space. The quickest way to finish off a Shadow is to simply activate Devil Trigger with the shotgun equipped. Once its core is revealed, use the Kick-13 combo while in Devil Trigger. If you prefer Alastor, you can use the Stinger combo. Waiting for its spear form is a good strategy, and may leave the core open to attack. However, on DMD mode this is simply a waste of time unless you're certain you can expose the core without waiting too long. Once enough damage has been done, Shadows will turn red and attack with even greater ferocity. If they catch you in their jaw-like form while in this phase, they will explode kamikaze style and deal a great amount of damage.
Facing off against more than one Shadow can be challenging, particularly if you have not fully upgraded Dante. However, it is vital to keep an eye on all of them if possible. If you only focus on one, you would leave yourself vulnerable to attacks from the others. Their corkscrew attack is both accurate and destructive, hence you need to know where they are at all times. Going into Devil Trigger can help here. By using Air Raid, try to force as many Shadows as you can into their core form, then use Vortex to hit all of them at once. Overall, using Devil Trigger can be a lot quicker to end a fight with these demons than ordinary attacks.
Avoiding the Corkscrew attack can take some practice, although you can simply roll to the side to dodge it or jump over it as the demon comes back down. However it can be a bit difficult to dodge, especially if you don`t see it coming (such as when fighting multiple Shadows). On harder difficulties this does massive damage so practicing dodging it is essential. The spike attack from the ground is not too difficult to dodge as long as you are prepared for it. If you're fighting more than one Shadow, it's best to be wary of the situation around you rather than the spikes.
On Dante Must Die mode, be quick about defeating them. If you are attempting "The Three Beasts" on DMD mode, make sure you stay far away from them while they're in DT mode. In this mode, the Shadows will automatically release their magical energy as opposed to firing it after being hit by Dante`s sword, with devastating results.