Stumbled upon this phrase. Dictionary as well as google does not yield any results. Example would be: 3年の威厳ってやつをガッといったってください。
I think this is ガッと言う rather than ガッと行く. While 行く sometimes takes を, 威厳ってやつを行く doesn't make sense here. 威厳ってやつを言ったる is roughly the same as 威厳というものについて言ってやる.
Either way, ガッと言う and ガッと行く are both used, and the meaning of the ガッと part would be the same. ガッと (also written as ガーッと) is a Japanese mimetic adverb that describes how an action/word is vigorous, powerful, quick or sharp. It's perhaps dialectal (I feel Kansai speakers tend to use it more often).