Did Tigerstar killed Bluestar on her last life?

No. He tried to in Forest of Secrets, but Fireheart(Firestar) stopped him. Bluestar gave up her last life by attacking the lead-dog who was about to kill Fireheart and knocking him, and herself over the side of the gorge. Fireheart jumped in and tried to save her, Mistyfoot and Stonefur helped, and when on dry land again Mistyfoot and Stonefur forgave Bluestar for giving them away. Bluestar told Fireheart about the prophecy 'fire will save our Clan' and said. "Fireheart, you are the fire that will save ThunderClan" Then she died and went to StarClan.