How was Undyne able to resist dead in the genocide route if monsters can't have determination?
This is actually a misconception. Nothing in the game states that monsters cannot have determination. It’s actually a case where monsters cannot handle determination like humans do.
Here is the the unused lab entry about the amalgamates.
ENTRY NUMBER 17monsters’ physical forms can’t handle “determination” like humans’ can.with too much determination, our bodies begin to break down.everyone’s melted together…
This information is echoed by what Alphys says to Frisk in the true lab.
From these two, it’s clear that physical matter is required to handle determination, and “monsters’ bodies do not have enough… physical matter” to handle the excessive amounts of determination that humans are capable of. This lines up with the comparison between humans and monsters’ physiology.
» read more: monster physiology
Humans have physical forms that allow them to handle high concentrations of determination. Their physical forms make them stronger than monsters. However, monsters must have some physical matter to them if they’re not all magic. Moreover, there are a few instances in game where monsters are said to have determination.
GERSONUndyne? Yeah, she’s a local hero around here.Through grit and determination alone, she fought her way to the top of the Royal Guard.
ASRIEL:With everyone’s power… With everyone’s determination…It’s time for monsters…To finally go free.
UNDYNE:Now, human! Let’s end this, right here, right now.I’ll show you how determined monsters can be!Step forward when you’re ready! Fuhuhuhu!
Undyne is able to resist death because of her determination, similar to how a human’s soul persists after death. But why would she only become Undyne the Undying in the genocide route?
One possible explanation is that in the neutral route, Undyne does not have enough determination to become Undying. While this clearly contradicts the idea that monsters cannot handle excessive amounts of determination, there is one important thing to note in the genocide route: Undyne’s body is “reformed.” Her body literally breaks apart upon death and is recreated to become Undyne the Undying. This is thanks to her determination to save not only the monsters, but the humans as well – “to save Earth.”
On the other hand, in the neutral route, Undyne is only fighting for the monsters in the underground. After losing all her HP, her body melts because she is trying so hard to defy death with her determination – her “will to keep living.” Unfortunately, it’s not enough to reform her body.