The 15-day time gate is one of the required acheivements. If you click on the main achievement (Path of the Ascension III), it shows exactly which 11 achievements you need to complete.
You say the season is too short, but there are currently 39 days left this season – enough time to complete not only part III’s timegate, but also part IV’s. You can also start working on the part IV timegate as soon as you complete the part III timegate, even if you haven’t finished the main part III achievement.
As for the divisions, you won’t need to cross the divisions again – you need to cross 10 divisions in total across the 4 seasons split in whatever way you like. Each achievement doesn’t need to be completed within a single season – the only exception is Exalted Legend, but that’s not part of the backpack achievements anyway.
