Skyrim potions for boosting alchemy skill

Solution 1:

There is, but it's really suppose to be a bug

The Fortify Restoration enchantment erroneously boosts Fortify Skill enchantments. You can then create a Fortify Alchemy armor, make some Fortify Restoration potions, drink them, and your next Fortify Restoration potion gets stronger.

Keep doing this and you get absolutely insane increase.

This bug is fixed only in the Unofficial Skyrim patch. The official vanilla game still has this.

Solution 2:

There are no potions in the base game or any of the DLCs that can have the Fortify Alchemy attribute on them (bring mods into the mix and all bets are off).

However, there are potions with the Fortify Enchanting attribute, and there is a Fortify Alchemy enchantment. Before you ask, yes, this does allow you to loop the two to gamebreaking levels.