There are a lot of comments for Tserrina that indicate if a bat is see invis, that Tserrina will pop, or that if a pet can't attack it, Tserrina will pop. That may have been true back in the day on live, and that may be true on P99, but it is most certainly not true on Agnarr. I killed Tserrina over 65 times (I checked in my logs with gamparse) before a robe finally dropped for me. My pet was able to attack every shrouded bat, and there was no rhyme of reason regarding whether or not the bat saw invis. Additionally, there were several times where the bat did have noticeably lower hit points than the others, but this did not always guarantee a Tserrina spawn.
Contrary to what other posts will indicate, Tserrina was also able to spawn on other floors. There are 5 bats on the 6th floor, so I made sure to clear those as well. Bats can spawn on other floors, although it is very uncommon. I have personally seen bats on floors 1 and 4, and I watched Tserrina spawn on the 4th floor.
That's my $.02