Why did Chief Phillips try to kill Willard?

This is an interesting question and quite an intense moment indeed. Yes, it does very much seem like he is actively trying to kill Willard by pulling him towards him. But it's not necessarily envy for the living, or not in general. You don't generally see soldiers trying to drag their comrades into death with them, rather on the contrary, they'd try to protect their teammates even when dying.

And in fact this brings us to the true reason he tried to kill Willard. Captain Willard was not part of his crew, in fact he was (at least according to Chief Phillips) responsible for their certain deaths.

Then there was Phillips, the chief. It might have been my mission, but it was the chief's boat.

From the very beginning Chief Phillips was opposed to Captain Willard and his mission. For him, Willard basically took his boat and his crew and went with them on some obscure top secret mission noone else in the crew was allowed to know anything about. At various moments throughout their odyssey Phillips questions the value of the mission, but he's bound to Captain Willard's command.

Phillips: These boats are running supplies. I'm going to take a look.
Willard: Chief, my mission's got priority here. You wouldn't be here if it wasn't for me.
Phillips: Until we reach your destination, you're just on for the ride.

And then at the end basically everyone on Phillip's boat was about to get killed in an attack, including Phillips himself. And for what? For nothing! For some useless suicide commando in the middle of nowhere. And at this point Chief Phillips tries to kill the man who dragged them all there with him and make him pay for what he brought upon them (and possibly also to end this mission there and then and maybe save his remaining crewmates this way).