Early on, your best investment is the Black Hole. Place it in a corner of the screen and tilt your device so that Buddyman will regularly fall into the hole. Eventually, once you have more coins, you can combine that strategy with some abuse from a weapon like bacteria or adrenaline guns to thoroughly ruin Buddyman's day.
Weaponize
As the game starts, your only tool for doing damage to Buddyman is your finger. Knock him out and you earn free coins, plus an offer to watch a video for even more of them. You should be well on your way to purchasing a weapon by then, and once you do, you can really start having fun dealing damage to Buddyman.