The correct answer is: A. A is liable to indemnify B for those damages.
An indemnity is a promise to reimburse someone for losses they incur as a result of something you did. In this case, A employed B to beat C, and agreed to indemnify B against all consequences of the act. This means that A is promising to pay B for any damages that B incurs as a result of beating C.
B did beat C, and C is now suing B for damages. As a result, B is likely to incur damages. A is therefore liable to indemnify B for those damages.
Option B is incorrect because A is fully liable to indemnify B, not partially liable.
Option C is incorrect because A is liable to indemnify B, not not liable to indemnify B.
Option D is incorrect because A is liable to indemnify B, not none of the above.