Here is the full list of all 13 YANKAI'S PEAK. achievements.
Complete YANKAI'S PEAK.
Complete all levels in Part VI and earlier.
Complete all levels in Part V and earlier.
Complete all levels in Part IV and earlier.
Complete all levels in Part III and earlier.
Complete the sixth bridge.
Complete the fifth bridge.
Complete the fourth bridge.
Complete all levels in Part II and earlier.
Complete the third bridge.
Complete the second bridge.
Complete all levels in Part I.
Complete the first bridge.