The Blood Diary, which can be found under "Player>Books>Blood Diary", is a public page that displays how many enemies of each type you have killed.
For a creature to count toward your completion total and be listed, it must meet the following conditions:
Aside from direct battling, you can also send creatures on an adventure to a given dungeon to claim kill credit for both the normal enemies and Uber Enemy present there.
Show off your Blood Diary to friends by copying the URL. It's public so anyone can see how many creatures you've killed!