The translation from the video got it right, it means "bêbado" (embriagado, inebriado, alcoolizado, cheio de álcool no sistema
It can also be used in a ironic/joking way, as in "We were tanked up on gin and orange juice."
(estamos bêbados de gin/gim e suco de laranja.)http://idioms.thefreedictionary.com/tanked
And, as you see it can be worded "tanked up" (on something).