Then comes the end, when he delivers the kingdom to God the Father after destroying every rule and every authority and power. For he must reign until he has put all his enemies under his feet. The last enemy to be destroyed is death. For “God has put all things in subjection under his feet.” But when it says, “all things are put in subjection,” it is plain that he is excepted who put all things in subjection under him. When all things are subjected to him, then the Son himself will also be subjected to him who put all things in subjection under him, that God may be all in all.

God didn't literally kill death, it's pretty clear that it's saying he rose above death and subjugated it.

And all of this is supposed to be taking place at the End Times, not just some thing that Jesus did during his life.

"Killing" doesn't make sense, neither does "destroyed" as I saw in other translations, but I get what you are saying.