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