One of the most prominent alchemical substances was potash (potassium carbonate), which can be made by collecting regular old wood ashes, dissolving them in water and then drying up the water. (In fact, the word potassium comes from potash, or "pot ash".) You can use potash and animal fat to produce lye and soap.
Are there caves in the forest? Another nice material is saltpeter (potassium nitrate), which you can get by soaking bat guano and filtering the crystals out of it. If you don't have access to bat caves, you can produce saltpeter by collecting a pile of manure, mixing it into a compost heap with urine and wood ashes, letting it decompose, and then leaching and filtering the result with potash.
All you need to make alcohol is fruit and a place to let it ferment. Besides drinking, alcohol is useful as an antiseptic and fuel.
One substance you can't get from an ordinary forest, but would be an excellent find in your story, is sulfur, which is often found around hot springs. Sulfur and saltpeter, burned together in the presence of steam, lets you make "oil of vitriol" (sulfuric acid). Depending on what else you find natural deposits of, this can be used for a whole host of purposes, although this kind of strays away from the original question. But one thing that is worth noting: Sulfur, charcoal, and saltpeter is all you need to make gunpowder.