Why won't my module table populate
I can see a few problems at first glance:

'access callback' =&gt; TRUE, will mean everyone gets access no matter what and make 'access arguments' redundant.

The default access callback is user_access, which would accept your access arguments of array('access content'). So to use that just omit the access callback line.

$items['achievementList/list'] = array( is a strange path.
Generally best to keep it all lower case but that's not a requirement.

'page arguments' =&gt; array(1), will be passing in the string "list" to your achievementList_generate_table() function, but there is no point passing in a parameter that never changes and you arent actually using it, so just array() is fine for those arguments.

For more information I recommend reading all of the documentation for hook_menu().

The real problem though would be that your callback function is not returning anything for some reason.

(as per Clive's comment) I'm going to assume you are using Drupal 7.
In which case your call to the theme() function is incorrect.

In drupal 7 all variables going into the theme function should be in an array, so your line should look like this:

return theme('table', array('header' =&gt; $header, 'rows' =&gt; $rows));