Tetra in general are nippy fish. They attacked betta out of their own habit of nippy nature. Betta's long fin makes it a great target. Tetra are also generally faster than betta. The poor betta doesn't stand a chance although it does bear the name of "Siamese fighter fish". It is the victim here.
Corydoras catfish are also schooling fish. They will also be shy if you don't give them at least 5~6 in number. Keep in mind if you get both corydoras and cardinal to 5~6, your fish tank will be overstocked. Personally, I wouldn't put anything other than bottom feeders such as corydoras in the same tank as betta just to protect the betta. You might be in a hard situation since you already have cardinal tetra. It is your choice to up the number of cardinal to 5, or get rid of the cardinal and get 5~6 cory instead.
