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The Government Gimps is a GTA 5 Secret Achievement. It is an achievement/trophy that you can easily acquire while playing the games campaign normally.
To get this achievement/trophy, the heist The Bureau Raid needs to be completed.
(A guide to completing this heist a different way can be found here.)
Once the heist is complete (with the firetruck, you drink some 'incest juice'), you should be awarded with the achievement/trophy.