I've already completed all the achievements except for the last one (Amy's Achievement) and suddenly a huge trouble appeared. Every time I collect a Giant Ring, game freezes for about 15 seconds (regardless if I already have all the emeralds or not). Also identical freeze appears when I try to start a new game.
UPDATE: I had killed the application while frozen and lost saved data. Luckily I had a restore point from two days ago. It doesn't freeze anymore so now I can try to reproduce it...
UPDATE2: I tried to repeat the actions I took before the problem started and I managed to reproduce it. First I defeated the final boss with Amy (just the Final Fight from All Clear menu that is), then I went with her to the statue in Rusty Ruin where I was unable to complete the achievement (guess I have to complete the entire game once more, don't I?). After that I started a new game as Amy and that's when the first freeze occured.