An exclamation used in response to a situation that so far exceeds all normal levels of awesome that the only natural form of celebration is to have a cocktail.
Can also be used as a sarcastic response to something that is driving you to drink.
Note: An upscale, sophisticated relative of “awesomecake”
Celebratory: It's taken me years but I finally made it to Level 3...awesometini!
Sarcastic: So, it's 6pm and I only have 4 more hours of work today...awesometini.
Note: When going with the sarcastic usage, it's best to insert a dramatic pause between "awesome" and "tini"