How to push form values to database in Drupal
You're not far off, a couple of things:


Creating a table like that in an init hook is definitely not recommended; Drupal provides hook_schema() so you can describe tables to the system. Uninstall and install your module again after implementing it and you'll see the table appear.
The reason your insert is failing is because you have a NOT NULL integer field which you're not providing (achvmntID). Drupal has the serial field type rather than an AUTO_INCREMENT key to get a serial field:

'achvmntID' =&gt; array(
  'type' =&gt; 'serial', 
  'unsigned' =&gt; TRUE,
  'not null' =&gt; TRUE,
),