Here is the full list of all 48 Jump King achievements.
Reach the top.
Be happy you have a helmet. (1000 Falls)
You are a seasoned jumper. (10 000 Jumps)
Reach Chapel Perilous.
Enter through an illusory wall.
Find the room of The Imp.
You have much to learn... (1000 Jumps)
If only you knew... (100 Falls)
My lord is a true veteran in the art of jumping! (20 000 Jumps)
You have heard a taste of the old man's wisdom. (Listen to Old Man 10 times)
You have heard all that the old man has to teach. (Listen to Old Man 40 times)
Hear the advice of the hermit on the mountain. (Listen to Hermit 10 times)
Each man has his price? (Talk to the merchant 4 times)
Complete the game within 1 hour.
Complete the game within 15 minutes.
Finish the game wearing the crown.
Finish game wearing the special boots.
You seem to dislike birds?
Complete the game without falling.
Own the special boots.
Only the finest for a King.
That bird...
Complete game with giant boots.
Complete NB+ with giant boots.
Complete the game with Snake Ring.
Complete NB+ with Snake Ring.
Complete New Babe+.
Complete New Babe+ without falling.
Purchase the Giant Boots.
Recieve the Snake Ring
Reach Deep Ruin.
Find the hidden nose.
Wear the Snake Ring and the giant boots at the same time.
Complete Ghost of the Babe.
Complete Ghost of the Babe with only 2 falls.
Many thanks, brother!
Find the 9th cat.
Complete Ghost of the Babe within 1 hour.
Complete Ghost of the Babe within 30 minutes.