The scoring system is definitely confusing at first. The general strategy is to collect all the balloons under the largest kind of combo possible, and sometimes it means careful setups. This one is a little more straight forward, so I'll leave my full strategy and thought process in the spoiler (though there may be others that work).
The basic idea is that I collect the first info balloon with no shots, the six tunnel blues and first set of nine reds with my first shot, and then the second info balloon and second set of nine reds with my second shot. (100+1+3*15+3*10-2=174)
The first balloon is forced to be popped out of combo. There are 25 balloons remaining. If you could pop 20 or more of them in one shot, you would get a quadruple combo, but this doesn't seem to be possible. Therefore, we have to rely on triples. This means that both of our shots will take out more than 10 balloons. The first shot can therefore only take out a maximum of 15 - to leave 10 at the end, which is conveniently the maximum in the area that is easy to reach in one shot. It is annoying to land this first shot and I'm pretty sure it has to land in the correct spot (which for me was almost on the left curve). After this, you can hit the info bubble balloon and the nine at the bottom with a very precise and lucky shot and it will complete a 174. This second shot is why this one sucks, I had to retake the first shot 4 times to land in the correct position and even then it was very precise so IDK if I was just missing or some spots you can't make the second shot work.
I don't understand the scoring system very well in HP. Is the aim just to get the highest combos possible in the fewest amount of shots? If that's the case, my brain is gonna struggle to look at the levels and work out the optimal way through them. Maybe I just need more practise... Congrats on the successful grind though!
The basic idea is that I collect the first info balloon with no shots, the six tunnel blues and first set of nine reds with my first shot, and then the second info balloon and second set of nine reds with my second shot. (100+1+3*15+3*10-2=174)