I am contesting my deceased brothers insurance beneficiary

An insurance policy, including the beneficiary designation, is a contract: the policy pays to whomever the terms of the policy state should be paid. If he had not finalized the change fully, the policy must pay to the person still designated as beneficiary, even if your brother wanted and was starting to change it. The insurer MUST pay as the policy directs, so if the change was not yet made, there is likely nothing you can do.
However, if your brother did *everything* he was supposed to do--it was final as far as his responsibilities to provide information, sign, approve, etc. and there was *nothing* left for him to do--the fact that the insurer was slow in doing its part should not prevent the change from going through. In this case, where there was nothing at all left for your brother to do, you may be able to file a lawsuit as the 3rd party beneficiary and force the insurer to pay out as directed by your brother. (You are strongly encouraged to hire an attorney to help you do this.)
But we have to stress, this would only be the case if there was literally nothing left for your brother to do. If he still had to sign or approve something, then he did not complete making the change and the prior beneficiary is still the beneficiary.