+1 for the screwdriver/small Allen key trick.
@Sprite71 My Doggys used to get stuck fairly regularly. It was one of the reasons I gave up using them. It really is piss poor design to have an afc which spins through 360 degrees when there is nothing else to hold the base with when unscrewing the tank. Two simple designs to solve the problem would have been a notch on the base with a corresponding lug on the afc as used on the Cloud One, or the pin on the base and corresponding recess on the afc as used by the Hussar.
With regard to the top, I had the same problem with one of my Doggy clones. The chimney should unscrew from the top cap, but mine was so tight I had to resort to using pliers to separate them. I used a pair of small slip-joint pliers on the top cap at the same time using small needle nose pliers to hold the bell inside the tank. *If you do use pliers, make sure you always have some cloth between the plier jaws and the component, to avoid doing any damage*. If you hold the bell steady, the top cap should unscrew if you turn it anticlockwise.
(edited to include poster's name)