I can point you in the right direction:
1) Look in /plugins/achievements/templates/achievements/achievements/ and look through all the files for the word you want to change.
2) Copy just the files you’ve identified into /themes/YOUR_THEME/achievements/ — where YOUR_THEME is the theme you are using, and you’ll probably need to make a new sub-directory called “achievements”. Just copy the files in there.
3) Edit those copied files in a text editor. In your case, you can just dive in and change the wording. Save the files.
That should be it.