Here is the full list of all 15 Hero Generations: ReGen achievements.
Build a Monument building next to any town.
Survive for 5 Generations.
Reach 5,000 Fame in a single hero lifespan.
Reach 2,000 Fame in a single hero lifespan.
Reach 10,000 Fame in a single hero lifespan.
Reach 20,000 Fame in a single hero lifespan.
Reach 30,000 Fame in a single hero lifespan.
Kill A Boss Monster in combat.
Discover and kill the End Boss Monster.
Visit all 6 world biomes in a single lifespan.
Earn 20,000 Gold in a single hero lifespan.
Survive for 10 Generations.
Survive for 20 Generations.
Survive for 30 Generations.
Survive for 50 Generations.