Was injured badly

[Sped Tiger]

Could you say if all are correct?
1.
a. The little kitten was badly injured;
b. The little kitten was injured badly.
2.
a. I was really tired;
b. I was tired really.

 

[Barque]

1a and 2a are fine.
1b sounds odd to me.
2b isn't fine if you're using "really" to mean "very" (as in 2a). It could work if you mean "actually" or "as a matter of fact".

Don't take this as the basis for a rule. There are other adjectives that can be followed by "badly". "He was treated badly" sounds better than "He was badly treated".