Hi there,
The plugin is i18n translation ready which means you can change the default translation for English. There are some manual steps required to do this though. See here http://codex.wordpress.org/Translating_WordPress. You may want to install a tool called Poedit.
You can simply change the Assignments text to display as Achievements instead. Line 570 of buddypress.php file in badgearoo/includes/integration path. I do not recommend modifying this file directly as it will be replaced on update.
The .pot and .mo files are located in the languages directory of the plugin. The text-domain of the plugin is badgearoo. Remember when translating to name the files in the format <plugin name>-<locale>.<po or mo> e.g. badgearoo-en_AU.po.
Daniel