וישמע יתרו: מה שמועה שמע ובא, קריעת ים סוף ומלחמת עמלק
Now…Jethro���heard: What news did he hear that [made such an impression that] he came? The splitting of the Red Sea and the war with Amalek.
The question is why did he need the war with Amalek if he had The splitting of the sea?
In one of his talks, the Lubavitcher Rebbe zt"l explains:
The Splitting of the Sea was the first intimation that the physical and the spiritual could combine (which ultimately became a reality a few weeks later, at the Giving of the Torah), since "the sea" represents the spiritual worlds that are hidden from our ken (like the depths of the ocean), while "dry land" symbolizes the material world that is revealed to our gaze.
On the other hand, Amalek's attack on the Jewish People demonstrated that this unity between the two realms is far from complete.
So Yisro, realizing this, understood that it would be up to him to come join the Jewish People in making this a reality. He was uniquely qualified to do so, as his era's prime expert on all idolatrous deities (i.e., manifestations of materiality), who would now come and acknowledge that G-d creates and maintains all of existence.
I've also heard another explanation whose source I don't now recall (it's sort of similar to a comment in footnote 33 there, but taking a somewhat different tack):
After the crossing of the Yam Suf, all of the nations of the world were deeply impressed by the display of G-d's power, and were afraid to attack His people. Until Amalek came and recklessly "jumped into the boiling tub," thereby making others less nervous about doing the same (Rashi to Deut. 25:18).
Well, then, this set Yisro to thinking. If even after such an awesome demonstration as the Splitting of the Sea it's still possible for there to be an Amalek who ignores the whole thing - why, then, this shows that one can't just be impressed by it and remain as he was; sooner or later this excitement will evaporate, cool off, and then one may descend to the level of an Amalek. He has to act, now, while the impression is still fresh! And that's what he did.
The Gur Aryeh says that all the other miracles Yisro saw were localized, but these miracles affected the whole world. Rashi (Shemot 14:21) previously stated that all the water in the world split when the sea split. Rashi (Shemot 17:12) also says that during the war with Amalek, Moshe stopped the sun from setting.
When Yisro saw that all the water split, he understood that this wasn't a bunch of miracles, but rather one miracle, that G-d split the element of water (which naturally affected all the water in the world). He therefore understood that G-d had mastery over the earth. The stopping of the sun showed him that G-d had mastery over the heavens.
Yisro understood that G-d was in complete control of the world, and decided to come and join the Jewish people.
The Maskil LeDavid explains that it was specifically these two miracles that explain why Yisro decided to come to the Jews.
Yisro had already given up idol worship a long time before (Rashi Shemot 2:16), but thought that there was no difference between the Jewish People and a non-Jew who worships G-d.
Then he saw how the whole world was scared of the Jews after the splitting of the Red Sea, including the Chieftains of Edom (Shemot 15:15) (of which Amalek was a part of). Why then, would Amalek attack the Jews, it made no sense, unless the Jews had sinned (Rashi 17:8), and G-d was punishing them.
But if G-d was punishing them, why would He prevent the Jews from being defeated by the Nation of Amalek? It must be because He loves the Jews so much that he is willing to forgive their sins.
When Yisro saw this, he wanted to be a recipient of that love, and traveled to join the Jewish People.
Another answer is provided by the Zera Yackov The Gemara in Yevamous says:
רעה תבא למקבלי גרים
The Tosfos Ri says on this That we send him away or accept him Right away but if he keeps asking we accept him as we see that Avraham Yitzchok and Yackov did not accept Timna when she came to convert so she went and became a concubine for Elifaz the son of Eisav and that is where Amalek comes from. It comes out from Amalek we learn out to accept Converts.So now that Yisro saw that Amalek caused the Jews much Suffering now they will be more accepting of him as a convert that is why Yisro needed both The splitting of the sea and the WAR WITH AMALEK.
