I have a MSSQL 2008 .bak file from a database that I need to migrate to MySQL. Is there some way to do this without having to install Window$ and SQL Server there ? Other options would be to do the migration online, even though that would take some time, what would be the best tools for that ?
Installing a Windows Server evaluation version and an SQL Server evaluation or Express version (if your BAK file is under the maximum size for the version of SQL Server Express that you intend to use) is going to be the method that will provide you assured integrity of the data you're trying to export.
I'm not aware of any Free or no-cost third-party methods to read SQL Server "BAK" files, but since you can obtain all the tools from Microsoft to perform the export at no-cost anyway I'm not sure why you wouldn't want to use their tools. You're going to be assured, with their tools, that the data you export from the database is correct.
In this answer I'm assuming that you're talking about migrating some data in tables and that you're aware that more advanced features aren't going to just seamlessly migrate from Microsoft SQL Server to MySQL.