Wanted to point out a few different things to help with obtaining this achievement.
1) If you have the "Disc Extender" DLC, the stars you earn on the extra 9 levels will count towards this achievement. That way, if any of the cycle levels are giving you trouble, you can earn a few extra stars on disc levels 17-25 without worrying about three starring all cycle levels.
1B) It has been confirmed that if you have the OUTLANDS pack, stars earned in that pack DO NOT count towards this achievement as noted by Elite Shadow 87.
1C) It is currently unknown if stars from the CYCLE EXTENDER pack count towards this achievement.
2) In order to three star all disc levels, you will eventually need to purchase the bit doubling power-up and point doubling power up. Once you get to the later levels it becomes impossible to get three stars even if you keep a bit chain going for the entire level. I believe it was around level 10 when I realized even with a perfect run there wouldn't be enough points unless I purchased the point doubler. For levels 15 and 16 I also needed the bit doubler to assist with getting my bit multiplier high enough. And o top of that, in order to three star level 16, I had to make sure I picked up three or four power-up cubes along the way.
3) I found cycle levels a pain the first time I played through them all. I was only getting 1 star even when I thought I had a pretty good run. Then I realized that my score was suffering because I was dropping my multiplier chain mid-way through the level. While it is technically possible to have a perfect bit chain from start to finish on every cycle level, there are many sections where even the slightest mix-up will cause you to drop your chain. Then I discovered the Bit Compiler companion. It will pick up nearby bits even if you don't drive close enough to them to pick them up yourself. Once I started using the Bit Compiler I three starred cycle levels 2 through 11 on my first attempt. The Bit Compiler made it almost impossible to drop a multiplier chain.
4) Without a doubt, the most frustrating sections of the game for me were the tank parts. I would have a great bit-chain going, and then the tank section would come along and I'd take damage. Or I wouldn't take damage, but I wouldn't be able to destroy the tank quick enough and a purge would happen. My strategy on the tank sections is to basically continually move back and forth from one edge of the platform to the other. When I'm near the edge, I'll wait for the tank to shoot, then I'll run across to the other side, shooting the tank in the process once I've cleared the tank's projectiles. If there's an "electrified" floor, you should be able to jump and glide the entire width of the platform you're running on, landing on a normal floor section.
If anyone has any questions/comments/etc. let me know and I'll do my best to respond in a timely manner.
P.S. I'm currently working my way through the Disc Extender levels. I've three starred 17-20, and the remaining 5 are definitely going to be a challenge!