Guys V is 'turnbased' (his theme is chess for a reason).
Turns can be taken by Cat, Bird, V. Changing target is important for getting rid of pet-cooldowns.
A turn is something like: starting a move, or ending it. In the case of Bird: shoot is a move (press button), and barricade is a move (letting go of button).
Then you can 'wrap' cat moves and V moves in bird moves, and vice versa.
The 'issue' with V is that it is very easy to shoot yourself in the foot, aka not making a clear chain of moves.
The way to start solving this is to be precise with lockon, or be very precise with the directional stick. Consider Bird: buttonpress without lockon will target a mob that is (potentially) different from the mob currently under attack from Cat.
Devil Trigger (supercharging your pet) is synonymous with changing target, it allows you to 'cheat' a move where otherwise you would get halted by a despawning pet.
It was always intrigueing to me that one of Nightmare's moves has in the description something like: if you keep the button pressed then x. (I think it's the laser beam). It makes sense in that you can then control Bird and Cat while the laser keeps going.
Enemy step is also very important, despite what the game itself wants you to think.
Try this: hold cat or bird, and then alternate the other pet and V.
The game is played by properly (=in the right order, at the right time) pressing, holding, and letting go of cat/bird/v/jump/DT/Nightmare. The problem is that IF you make a mistake, it all falls apart.
I suspect that for bossfights, the time that is allotted between the final kill-move, and the actual destruction of the boss, allows for some orchestration of the pets.