I have heard people saying that Netzahualcoyotl personally fought assassins more than once, this sounds like an urban legend, however, it is strange that he, having relatively few resources (specially after Maxtla captured the aztec tlatoani) was able to avoid assassins and bounty hunters by some of the most powerful people in the whole world back then, and yet we know he did it, how?
The first time around he did so by hiding on top of a tree while his family was killed by the assassins sent by Tezozomoc, later on his life, as he became a young man, he was politically "protected" up to a point by Maxtla's aunt due to Netzahualcoyotl having familial ties to her through his mother (women in nahuatl societies could command no small amount of authority), leaving Maxtla with little choice but direct confrontation with him as a means of ritually killing him (Netzahualoyotl was part of the mythical Tollan descendants so Maxtla couldnt just openly kill him at this point, he had to ritually defeat and "disarm" him before killing him), also bear in mind that the assassination of Netzahualcoyotl's family was already considered highly dishonorable and illegal, and drew a lot of political difficulties to Tezozomoc, though unlike Maxtla, he probably didnt care at that point in his life (he was said to be over a hundred years old and so fragile he had to be carried around in a cotton basket, a veritable mummy at this point).
Maxtla also wasnt in the best position possible, he technically wasnt the "legal" heir to Azcapotzalco, that being his brother Tayatzin, and on being made Tlatoani he had then pursued an imperialistic policy, by taking direct control over polities under his rule (in Mesoamerica, Altepetl leadership was usually chosen by a kind of indirect democratic-ish process), effectively breaking the current Triple Alliance (Azcapotzalco, Colhuacan, Texcoco), and alienating other powers in the Valley like Otumba, Zunpango and most importantly their ally Colhuacan who will refuse their calls of help once the war starts.
Curiously Moctezuma II would take almost identical actions during his reign on the run up to the war with the Spanish, and suffer almost identical results.
At this point Netzahualcoyotl has already rallied the support of the Tlaxcaltecans, Xochimilco and part of the pipiltlin groups of Tenochtitlan (though the Tlaxcalans as the Tlaxcalans were keen on doing, reneged on their promise when the time came, and the Xochimilcans were deliberately slow to respond, until the Mexica had done the heavy lifting of the war).
Notably as well, he himself should have had no small amount of martial ability as during the prelude to the war that would bring the new Triple Alliance into prominence he was able to sneak into Azcapotzalco and personally declare war to Maxtla in his throne room and then escape the city into Xochimilco.
Source: Chronicle of Mexico by Fernando de Tezozomoc (this one, not the evil mummy one)