Weyer's Tonic is a life-extending potion that Agrippa requires in order to escape. The potion was designed by Agrippa's student Johann Weyer.
The Potion has three main ingredients:
Acquiring the ingredients
Tampter is the saliva of the Kaernk (the water creature) that can be encountered in the Cellar Archives and the Cistern. To acquire it, one must go to the room adjacent to Agrippa's chamber, climb up the wooden stairs and find a haunch of meat. After that, you must go into the small room with the well (after you have opened the two doors in Agrippa's room), which is located near the Transept. There, the meat is attached to the well and lowered, where the Kaernk will devour it, leaving the bone covered in Tampter. If you miss this step before being captured in the Chancel, there is an additional Kaernk in one of the wells in the passage between the cells and the first room of the Nave (after you escape from the Shadow).
As for the vitae, it is acquired by distilling the blood of a tortured human being. In the Transept, by ascending the spiral staircase, you will find Alexander's study where there is some string on the desk. Attach this string to the glass jar. In one of the torture chambers in the Transept, you will find a drainage pipe covered by a grate. Open the grate, lower the glass jar into the blood and retrieve it. If you miss the blood in the Transept before it's blocked off there is another grate in the room that opens up next to Agrippa's room (cannot do this before being captured). By boiling the blood in the laboratory, you extract the vitae.
The fungus with the poison gland can be found in the Choir, just before the entrance to the chamber with the Brazen bull . You can get the gland by breaking the fungus itself, either using a rock or the hammer and chipper from the Prison blocks. The poison is extracted in the laboratory as well. If this step is missed before the Choir collapses, additional fungi can be found if you attempt to re-enter the Choir after escaping from the cells (You will be unable to reach the Choir due to a cave-in, but fungi can be found at its base).
Making the Tonic
Note that the tonic CANNOT be completed before you are captured in the Chancel, and this capture in turn does not occur until you've gathered all six orb pieces. Upon your subsequent escape from the Cells and flight from the Shadow, the quakes will cause parts of the castle to collapse, making the Laboratory accessible.
In the Laboratory, you have to (in no order), boil the blood on the burner to extract the Vitae, place the jar under the vice, then put the poison gland in the vice and crank it until it is squeezed into the jar. Finally, put the jar under the contraption on the center table, and place the Tampter-covered bone inside of the contraption. This will steam the bone and put the Tampter in the mixture. The potion is now complete and ready to be used to free Agrippa.