Here is the full list of all 26 Next Up Hero achievements.
Summon 4 Ancients on a single level
Invest enough Prestige to trigger a random Rare Enemy while Starting a Game Venture
Successfully complete a Single Enemy encounter!
Successfully complete a Time Limit Trial Level!
Have your Hero Die
Complete a Venture with a 'S' Rank
Choose to Extend a Venture
Choose to Kill a Boss
Unlock 35 Abilities
Unlock 9 Prestige Characters
Summon 8 Unique Ancients
Defeat 100 Buckles
Participate in a completed Epic length Venture
Participate in a completed Long length Venture
Successfully navigate a Darkness Level!
Successfully complete a Mayhem Level
Defeat 100 Dark Heroes
Participate in a Venture which gets completed with at least 500 levels
Raise up the Echo of a Registered Streamer
Raise up 15 Echoes in a single level
Raise 10 of the same House Echoes in a single level
Control an Echo while Spectating
Complete 5 straight levels without dying on a single playthrough
Raise 15 Symposer Echoes in a single level
Kill 3 Enemies with 1 Prestige Paladrin Shield Throw
Get killed by every unique enemy in the game