Certain enemies are of course, unkillable, likewise, three are unspareable.
All unspareable enemies have a way to spare them now.

As for unkillable enemies:
Bomb encounters (that usually appear during mettaton's game show) will be treated as a spare if you use the ACT, while if you defuse them by FIGHTing it will treat it as a kill.
Both Amalgamates AND lost souls are unkillable, if you encounter them when a boss event should have occured (in toriel's boss area, papyrus boss area, etc) it will treat them as a kill if you have more than 1 EXP as a failstate for geno.
Asriel Phase 1 has a condition that will treat it as a kill if you keep using the fight button.
Asriel Phase 2 work like lost souls.
Mad dummy works the same as lost souls.
