This is a recent addition to PS+ that has taken me by surprise. Not only did it hit PS+ on its release date, but its really good. Velocity 2x is basically a shmup and a 2d platformer, where you switch between your ship, and your character to enter space stations in order to open up more areas for your ship to go, which are gated by force fields.
So no only is it 2 cool genres within one game, but as the title suggests, it's all about speed. The aim of most levels is to do it as fast as possible, and you have a bunch of tricks to help you. There's a teleport that can be used in both the shmup and platformer stages. It's mainly for traversal through walls, but can also be used to get through the levels way faster.
The shmup sections also have a boost, which lets you move the screen. So the player controls the screen scrolling.
There are leader boards too, so get to it! Especially if you have PS+, since this fantastic game is free for both PS4 and vita.
Platforming:
Shmup: