I changed (once again) to
awesome and AIR applications doesn't work here.
One of the apps I heavily use based on AIR is TweetDeck. So I tried old clients that were once an alternative like HootSuite but not having support for both kind of RTs (Native and Quote) is a pain in the ass.
Then I remembered I installed once TweetDeck for Google Chrome on my browser and never give it a chance, because it was not exactly the same as the AIR-based app. Now it only lacks proper relation between followers and no-followers in each account when there are multiple accounts configured.
So yesterday was the day to try it, the right day.
It even has notification support, and customized by column!