According to Rocket League's Website:
The new ball has three different phases, each more powerful than the last, that determine how much damage is done when the ball smashes into the floor panels. The second and third phases are activated by multiple Battle-Car hits, so the longer the ball stays off the ground, the more powerful it becomes. While the first phase of the new ball only damages one tile upon impact, the second and third phases can damage up to seven and 19 panels, respectively.
It appears that hitting ball multiple times without letting it touch the ground activates the different phases - allowing it to do more damage. I will note that the way it's worded makes it sound like the longer the ball is in the air determines what phase it will be in however.
You can find my first experimentation video here.* As I said in my comments, I think its a combination of the number of hits on the ball and the time the ball is in the air (the longer it's in the air, the less hits needed to change the balls phase), which would adhere (somewhat) to what was stated on Rocket League's website.
I once counted 7 hits for the ball to lose its shell and reach stage 2. I also counted 4 hits once for it to enter stage 2. I noticed after 20 hits the ball went to stage three (witnessed this twice - though I think the first time may be cut off from the video). I also reached stage 3 with less hits once (I don't remember how many), which is why I think the air time is also a factor. The ball only ever changed phases after being hit, and if it hit one of the opposing teams tiles, it would reset as it's supposed to.
Around the 2:30 mark in my video, I hit the ball into the air for a decent amount of time after it had just reset. I then hit it once more after it hit the wall and it switched to phase 2. That was only two hits total, but the ball was in the air for a good amount of time before the second hit, hence my reasoning of it being a combination of hits and air time. The same thing happens around the 2:48 mark.
My thoughts continued:
I've made a second video* showing my testings, and I still think its a relation between total air time and hits that determines when the ball will change phases. I've also noticed that lighter hits may not be counted. This doesn't mean that heavier hits influence if the ball will change phases, but that the hit has to be heavy enough for it to count. One thing I was consistently able to do was hit the ball once at full speed and cause it to gain some air time. My second hit after that would cause the ball to change its phase.
- The ball will change phases after it is in the air for a certain amount of time and is hit
- You must hit the ball hard enough in order for it to count as a hit to change it's phase
*Tested in private match with no bots or players on the default settings