To respawn the ender dragon, first you must kill the dragon for the first time. To respawn it, you need to make 4 ender crystals. To craft these you will need 4 sets of the following:
7 glass blocks
1 ghast tear
1 ender eye
Return to the end with the 4 crystals and place them on top of each of the long sides of the center bedrock portal like this:
This will prompt the recreation of the original ender crystals, making the dragon reappear. You don't need to kill it again for the achievement.