This is a mistake.We had a chat on tuesday evening because the Dwarf in the party was considering becoming a Trollslayer. As he is already a good way through veteran he would have almost all of the skills and talents there so could progress to Giantslayer quite quickly. But to get in you must have slain a Giant.
The reason for the mistake is how the career prerequisite is formulated.
To enter Trollslayer you do not need to have slain anything. You only need a reason for your disgrace.
To enter Giantslayer you need to have slain, not a Giant, but a Troll. But what you really need is to have failed to die at the hands of a Troll, and now you need something more dangerous to kill you since you haven't repented enough yet.
To enter Dragonslayer you need to have slain a Giant and still feel disgraced enough.
To enter Daemonslayer you need to have slain a Dragon.
If we instead formulate what you seek out to slay (or, more properly, be slain by) things become straight-forward:
To enter Trollslayer you need to seek out death at the hand of a Troll.
To enter Giantslayer you need to seek out death at the hand of a Giant.
To enter Dragonslayer you need to seek out death at the claw of a Dragon.
To enter Daemonslayer you need to seek out death at the hand of a Daemon.