Her armor and her zero suit are the only clothing she has. She can't swim in lava without the gravity suit feature.
With the Varia feature malfunctioning, damaged, unaquired, or unusable, Undyne would be unprotected from the heat if in a super heated room with lava in it, and since she's part of the species of fish, the heat would definitely be a problem for her, especially if she's in a pool of lava without either her armor or her zero suit on.
Unlike regular fish, she can't stay in water for too long without her armor and zero suit.
If her armor is damaged enough, there's a 50% chance that she would instantly die.
She's thermophobic, which means she's afraid of heat.
Gaster had once saved Undyne from getting killed by a Space Dragon named Ridley. Ever since that time, Undyne had and still hopes that she will get a chance to return the favor.
Undyne has trusted Asriel, her husband, since they were kids.
Frisk is one of three apprentices of Undyne and Asriel, and sometimes Undyne would overprotect Frisk and the other two apprentices because they were originally from a different AU that was destroyed by Error!Sans.
Undyne always liked Sans because of his puns, so whenever Sans says a pun near Undyne, she would burst out laughing.
Even though Undyne and Sixbones are not truly brother and sister, they've always had, and still are in, an awkward friendship.
Undyne and Papyrus are somehow one in the same with personalities.
They may both be Undynes, but Undyne and Error!Undyne have a system which works like this: if Error!Sans decides to go destroy Undyne's universe, Error!Undyne would get to the universe before him, tell Undyne that he's coming, then she comes out of the house, and waits for him.