Satan didn't want to kill Jesus, he wanted to prove to God that everyone would disobey given the right set of circumstances. Most people will "compromise" (disobey) when faced with serious consequences, like death. All Jesus had to do was deny who he was and he could have lived. He wouldn't do it. He died because he wouldn't go against his Father's will.
Every time Satan faced off with Jesus he was unsuccessful. (Remember the three temptations in the wilderness?) The last time, Satan upped the ante and Jesus still didn't give in. Jesus knew how it would probably end up, that's why he was so upset as he prayed just before he was betrayed by Judas. He knew how hard it was going to be to remain obedient, that Satan was going to throw him into a situation where he (Jesus) would look like he was bringing shame on the very one he was trying to obey.
If Satan could prove that everyone would disobey then he would be right in stating that God was unjust. That's the whole goal, trying to prove that God is an unfit Father. ....and guess who wants the job???