A good translation of достигать/достичь(достигнуть) is "to reach". Their sets of meanings are almost coincide.

I'd say that достигать means that the goal or target is reached after some progressive motion towards it, and добиваться implies some concious efforts from the subject.

And yes, I like "достичь" more than "достигнуть" as well.

Examples when those verbs are NOT interchangeable:

Температура достигла 40 градусов.
Адвокат добился оправдания подзащитного.