Seems like there's a pretty defined process
outlined here
However, I'm guessing the agent either brushed you off so they wouldn't have to complete the form, or by accepting a reduced amount, you have no right to a future claim.
If there's a record of the damage being reported, you may be in luck to escalate, otherwise pretty sure AS will deny future claims based on this:
Baggage should always be inspected for any damage. We should be notified before you leave the airport. However, damage must be reported within 24 hours for domestic travel, or seven (7) days for international travel.
For damage covered by Alaska Airlines, an estimate or repair bill must be submitted within 60 days of your date of travel.
Links for reference:
here,
here, and
here