1. Shaul haMelech’s declaration to Shmuel haNavi, “Hakimosi es dvar Hashem!” sounds at first blush like either the height of chutzpah or the height of naivte. Shaul was commanded by Shmuel to kill every member of Amalek and to destroy their flocks and herds of animals. How could he possibly say that he fulfilled the dvar Hashem when Agag remained alive and all the animals were taken as booty?
The Alshich answers that the key words here are “Dvar Hashem” – not “divrei Navi.” Shaul knew that he did not do exactly what Shmuel had told him, but what Shmuel had told him to do was, in Shaul’s mind, not the dvar Hashem. Killing off the animals was an addition to the mitzvah, l'migdar milsa, but not the essence of the mitzvah of mechiyas Amalek.
So why did Shmuel think finishing the job, right down to killing the animals, was essential, but Shaul did not? And what of the mitzvah of listening to a Navi? Here the picture spills mostly outside the boundaries of what we know from the text and into the realm of more speculative thinking. I'll leave that to you (Ksav Sofer, Shem m'Shmuel, Sefas Emes all discuss; feel free to point me to other mareh mekomos).
2. On a completely different note, there are a number of Rabbonim who have written pieces on how we can enjoy a Purim after the horrific terrorist attack which occurred earlier this week -- read them; no point in me repeating the same points. Amalek is still with us, make no mistake about it. The Midrash writes that the "necheshalim" who Amalek attacked were the stragglers from sheivet Dan who were shlepping along outside the ananei hakavod, the clouds which were the visible evidence of Hashem's hashgacha. Amalek, explains R' Tzadok, preys on that feeling of being stuck outside Hashem's protection, unwanted, rejected, without hope. "Lo tishkach" -- the Koznitzer Magid writes that the word "tishkach" has the same letters as "tash koach," loss of strength. As difficult as times are, we need to respond with greater strength, greater bitachon, greater trust. Not an easy task.