G I A N T E G G! G I A N T E G G! G I A N T E G G! G I A N T WAAAA!

TL;DR - The game waits until after you've seen a "save game" screen to be done showing the info for boss levels' emblems and other stuff. After each boss, after that rainbow gate beacon "light-up" cutscene with the pyramid, you actually get put back in the boss arena with that area's chicken elder. You're meant to walk up to the chicken elder and talk to them for some dialogue emphasizing the rainbow gate (but not the 25-emblem requirement to actually beat Sand 3 when you reach the rainbow gate's door, ha). Instead of talking to the chicken elder, you can pause and hit "Select" to go back to level select. This also skips the opportunity to save your game (the blue boxes that Monkey mashes through after every other level's emblem tick and screen fade-out). On the next completed level, it ticks up to the boss level's emblem count for some reason. The emblem count on the level select screen is always correct, though. This "repeat" also goes for other info, like when you collect a GBA minigame item from hatching those eggs. The GBA eggs are located in most of the boss levels. So, you can get a "repeat" emblem tick and ALSO see the same pop-up message twice - the textbox for "You can now play [GBA minigame] in the Joy Carry." I could test whether beating a boss level as your last S rank, then skipping out of the level with "Select" can let you make the "You got all S ranks!" pop-up message and corresponding emblem tick appear twice. Glad you enjoyed the run!

@hakurou4620 I tried to reply, but it got long and auto-filtered out. Short version: after the good morning jingle/scoreboard, there's a "plate" of post-scoreboard info to serve. The plate only gets cleared after you get through a "save your game?" screen. After each boss mission, you can skip seeing the save-game screen by pausing and going to stage select. So, on the next mission clear, it serves the old plate of info. On stage select, though, the right info is still displayed (emblems, eggs hatched, etc). This also makes it so you can see the messages for "you can now play this GBA minigame!" twice.

Sure. The emblem count display on the tick up gets screwy for one level every time you pause and exit after the boss fights. The emblem still counts but the counter takes one full level to display properly

It's a GameCube game played on the Wii