Antonio1986

You had a good logic in that post but it's not really about that.

Both достигать and добиваться are not completed actions just because they're imperfective verbs but they also have perfective pairs to them - достигнуть and добиться - these are completed actions.

Yes, добиться and достигнуть are very very similar when used in the sense of achieve but there is a subtle difference though.

добиться (битва - battle) - this one emphasises that it wasn't easy for you at all to achieve something, that you went through a battle, struggle to get what you want

достигнуть - doesn't focus on what you went through to achieve what you wanted, it just states the fact of achieving

I hope this helps