Achievements are stored in another table, but the same problem can occur there. The frozen_hash column of that table stores local data for an achievement. In particular the still_not_right.at achievement stores all of the last answer data in that column (with some other data). That achievement can easily exceed the VARCHAR(1024) size limits. This is a known issue.
WeBWorK Main Forum
Data too long for column 'set_id'
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