I am asking this question, because last time link to Express Migration Tool 2.0 ( https://dev.sitecore.net/Downloads/Express_Migration_Tool/20/Express_Migration_Tool_20_Initial_Release.aspx ) is present on Sitecore 8.2 Update-1 ( https://dev.sitecore.net/Downloads/Sitecore_Experience_Platform/82/Sitecore_Experience_Platform_82_Update1.aspx ). All further updates does not show this link
The tool is not compatible with version newer than Sitecore 8.2 Update 1.
You should install install upgrade package using the UpdateInstallationWizard to upgrade from 8.2.1 to to 8.2.4
Officially the tool do not support 8.2 Update-4. However I have succesfully migrated to from 6.5 and 6.6 to 8.2 update 4. This was done on simple solutions, with limited or no usages of other features but the Sitecore CMS.
If you use WFFM or anything else like this, I would recommend using the tool to 8.2 update 1, and upgrade manually to 8.2 update 4.