It's not ambiguous -- most would understand what you mean. But it's kind of an awkward phrase, as it's not clear which definition of "claim" you mean to say:
"Claim" can be interpreted to mean "take ownership of something", where that something must be able to be owned. You can, for example, claim your luggage from the baggage carousel, or your phone from the Lost & Found. You can also claim you have certain rights, such as (in many countries) the right to legal counsel if you are arrested.
"Claim" can also mean "make a strong statement". You can, for example, claim that you will give up smoking, or that you own every Star Wars movie, or that you are the smartest, bestest President ever. It doesn't necessarily have to be true to be claimed -- the claim is just your own representation of some situation.
If you mean the first definition, then I would suggest using "assert" instead:
The teenager attempted to assert his autonomy while arguing with his parents.
If you mean the second definition, then I would suggest using "proclaim" instead:
The teenager attempted to proclaim his autonomy while arguing with his parents.