This Seeking Tech guide will explain how you can beat Blunderjaw in Astro Bot. Use the following video as a reference:
For the first step, quickly shoot down the two rockets. Afterwards, attack the exposed canister on his chest to end the first stage of the fight.
During the second phase, he will shoot out two rockets simultaneously. So, you will need to be even quicker in taking them out. He will then send out another pair that you have to dispose. Once you clear out the threats, attack the canisters on his arm and leg to end the second phase.
For the third section, Blunderjaw will shoot out five rockets. So, make sure you are fast and accurate with your shots. You may be able to take out multiple rockets at once since some of them are close together. Afterwards, attack the two canisters on his other arm and leg.
He will then send a tidal wave that will knock you in the air. Once you are airborne, aim for the canister on his head to end the main part of the fight.
Afterwards, move through the island until you get to the broken bridge, where the Blunderjaw will appear again. Wait until the canister appears on his chest and then shoot your arrow at it to end the fight.
Here is the same run again at normal speed.