It’s 400 points total to unlock everything in an elite spec training line – I just can’t remember off hand how many points folks have currently if they have done all the existing ones, but it’s right around 200. The rest you’ll need to earn in jungle to unlock the deeper skills/traits/etc. in the training line.
You only need 60 hero points to begin using your elite spec, the points you spend after that continue to unlock more skills, traits, skins, etc.
Again, hero challenges are worth 10 points each in the jungle. So no you don’t need to go do 200-400 jungle challenges.