How many badges are needed to upgrade legendary hero rank?

Rank	Cost	Total Cost
Rank 2	500 ~  × 3	500 ~  × 3
Rank 3	1,500 ~  × 9	2,000 ~  × 13
Rank 4	5,000 ~  × 31	7,000 ~  × 44
Rank 5	24,000 ~  × 150	31,000 ~  × 194
Rank 6	60,000 ~  × 375	91,000 ~  × 569

How to unlock all skills at level 10?

Badges	Comment
× 3 and  × 3	With 75% luck, there is a good chance to get Rank 4 and unlock all skills without leveling up