It is not purely luck, there are strategies you need to employ to get the hard badge. You DO need luck to get it and will need to grind over and over to get the luck, but if you keep at it you'll see the patterns of what you need to do. If the dev gave a better description of how to unlock powerups it would probably be easier for people.
Here's how you get the hard badge: You need to get a hole in 1 or a hole in 2 strokes every level except the par 5. This isn't as hard as it seems! You can quit a level part way through without losing your progress. So you take your shot (typically with an airboost and a power boost) and if you miss, quit, start round, select continue, buy your boosts, try again. this way you don't have to start all over if you screw up a level later in the game. One tip is that the boost to stop the ball mid air is very helpful. so you take a shot that will over-shoot and then stop it a few feet before the hole. it will still have spin and finish.
The game adds 5 seconds per stroke, so the key to getting this hard badge is low stroke count in addition to speed. Here is my plan. Play each level to try and get a hole in one or 2 shots. After each level, quit and practice the next round over and over until I'm relatively confident I can beat it in a couple strokes, and continue my previous game.
Yep, follow the advice to get the badge. I was consistently getting around 3.4 with no progress. I got lucky and wound up with the 3 green balls at the end and they happened to be all in a bunch. got to about 6 and got bored and lost for the badge.
Protip: If you get impatient and try and move a tile before the special tiles for that round loads, it will sometimes glitch out and mess up your tiles.