The alchemist's requirement for her last achievement/skill is max obedience.
For the alchemist the last thing I did was to go into the training menu and have sex with her. The requirement comes up as sexual love in my translate app so I assume that's what that did it.
The princes has the same requirement so try that on her as well.
The doll looks like it's asking for max love on the second requirement.
Let me know if those don't work.
Oh yea and this is the doll's favorite gift to help with her love raising if you need it.
View attachment 41830
Also was kinda curious why you have numbers here instead of letters here. Is that an option or something?
View attachment 41828
No I'm pretty sure none of them do.
You can buy bombs from the alchemist here.
They should one shot any normal monsters. Just make sure you are fighting the black silhouette fight with 2 monsters and not the one you recruit from as those don't seem to give EXP.
Just go to the highest tier area you have and farm the monsters there, that should work best.
View attachment 41829