Can you Recover Data from a Filevault encrypted harddrive externally? My mac won't boot and it maybe a harddrive issue, but I need to get the data off it, is it possible to recover the data using a set of tools if I know the password and have the appropriate cables?
What Mac are you using (Macbook Air / Pro)? Does it have a replaceable disk?

If the disk is not replaceable, I see the following options:


Access your Mac in target mode and unlock the disk from another computer. For example this article explains the procedure.
Using recovery mode: Press cmd + R : Recovery Mode
Same as above, but you manually select the recovery partition by pressing alt at boot


Sometimes the filevault2 volume cannot be opened easily. See here for a workaround.

If the disk is replaceable I would remove it, unlock the disk, and save the data e.g. with an USB-IDE adapter (like this one).