Each season is one calendar month long.
According to prominencepoker.com, the achievements do stack. So if you reach any higher tier, you'll pop the lower tier achievements also.
Simply finish the 3 provisional games at the start of a season. This will get your initial rank score assigned. You're guaranteed to be Bronze or higher, so this can't be missed after your Provisional games are done.
You can do this in either/both the Ranked Tournaments or the Ranked Head-to-Head modes. Each mode has its own Ranked score.