Papu-Papu is the first boss in the game. You shouldn't have any trouble with him.
To defeat him, as he is spinning around with his stick out, jump on his head. Repeat this for 5 hits in total until he is out of health and the trophy will unlock.
Personally, as his stick came around for me to jump in his direction and would land on him.
ScottishNub in the comments states "I found it easier to defeat him by standing on his throne". I have just tested this method and when he finishes his spin and slams down, he will miss every time. So you then just have to jump over and land on his head. This is the easier method although takes a little longer as you have to wait on him finishing his spins