To install Achievo, you need a webserver with PHP support, and a database server (MySQL is fully supported, PostgreSQL and Oracle support is present but may not be fully functional). Unzip the Achievo archive somewhere in your webservers' documentroot, and read the installation instructions (in the doc/INSTALL file after you unzipped Achievo, or online.
If you are upgrading from Achievo 1.1.RC3, an update of the source files will suffice. No database changes were made between RC3 and 1.1.0. If you are upgrading from an older version of Achievo, you should run Achievo's automatic upgrade script. After you unpacked the distribution using tar xzvf achievo-stable-1.1.0.tar.gz, see the UPGRADE file in the doc/ directory for instructions on how to upgrade your database. Upgrading is ofcourse not without risk. Don't forget to backup your data, and preferably perform the upgrade on a copy of your database instead of the original.