One has to establish first a Christological vision, of who is Christ, and only then venture to answer this difficult question.
I will be terse, just to give two variants of equally plausible answers.
Who is Christ? He is God's Logos who adopted, and eternally so, human nature. Since Logos is God (John 1:1-2), therefore it is correct to say that God became human. Now, Logos is Person, and Jesus' Person is that of Logos, so that Christ does not have another person but only that eternal Person of Logos. Nestorius, indeed, thought that behind the curtain of the word "Christ" two distinct persons hide: a) that of the Logos and b) that of the man Jesus, united in a most intimate manner; but this schizophrenic or better to say schizo-personic Christology was rejected in the Ecumenical Council of Ephesus in 429. Thus, the Person of Logos adopted not human person of Jesus, but human nature, and thus there is only one divine Person of Logos in Christ, who possesses after the Incarnation the human nature and eternally so, so that Logos now can be called also human, for He made His human nature as eternally linked and expressing His uncreated divine Personality, so that one cannot think already of this Personality in separation from the human nature He adopted, deified and eternalized. Thus, since the Person of Logos is uniquely expressed in the human unique body which He has received from Mary, then we can say that God died on the Cross, for this unique body is Logos' own body, uniquely expressing His uncreated and immortal Person through its created and mortal features, which features, through His dispensation were made His inseparable aspect, thus Logos is Jesus Christ and there is no separation between the Logos and man Jesus Christ, for both names refer to the same Hypostasis or Person, but in a certain ineffable and unmixed manner Logos also changelessly changed, for now He cannot not be without the unique body He received, which is part of His humanity. Thus, we also can freely say that God resurrected in third day, for God the Son is unimaginable already without His humanity, and His eternal Person eternalized the created bodily features as well, so even Jesus' body laying three days in sepulcher could be worshiped without any risk of idolatry, for it was already inseparable from the divine Personality of Logos. Paradoxically and ineffably, Logos never dies, but His body died, and in this sense we can say that impassible and immortal Logos suffered and died, in His body, while always being inseparably with His Father in Heavens. Vertigo of mystery, anything but easy and unparadoxical, anything but that which can be received without awe and trepidation.
Now, given that the Person of Logos adopted human nature, one may ask, what is this human nature? Is it only a body? Not of course (lest we fall into the blunder of Apolinarius, who thought that Logos inhabits just human body and Jesus does not have therefore human intelligent soul), because human nature is not only body, but also intelligent soul (I speak in categories of the classical philosophy of the Hellenistic culture, that was widely accepted in the time of Jesus). Thus, the Logos adopted not only human body, but also the intelligent soul together with this body. So, Christ is an indissoluble and unmixed unity of a) uncreated, eternal Logos; b) created human intelligent soul and c) created human body. This much about Christology, again, leaving very difficult and mind splitting nuances for another discussion, while now let us move to the 1 Peter 3:18.
Exegesis of 1 Peter 3:18:
When Jesus died on the Cross, what did in fact die? a) Logos Himself, b) Logos' created intelligent soul, or c) Logos' body? Correct answer must be that the c) is definitely right, for we can be certain that Jesus' body died. Now, could the Logos die? No! For Logos is God and God, per definition, analytically, to put it in philosophic language, cannot not be, or cannot die. Thus, the main question is: what happened to Logos' created intelligent soul? Did it die together with body and even more than body for the dead body was at least visible and touchable, whereas the intelligent soul disappeared altogether? I think, the passage very clearly suggests that this intelligent soul did not die together with body. Let me explain what gives me ground to claim the clarity of this point: if in "made alive in spirit" we put "spirit" with capitalized letters and regard it to denote the Holy Spirit, then that which is made alive - in the time when body lays dead for three days - cannot be anything else than the intelligent soul of Jesus. Why? Because, a) it cannot be body, which is still dead and thus not "made alive in spirit", and b) it cannot be Logos, which does not need to be vivified in Spirit, for He is absolutely equal to Spirit sharing full divinity with the latter and does not thus need Spirit for His vivification, being always necessarily alive for all eternity. Thus, if the "spirit" is understood as the Holy Spirit, we can infer that Jesus' intelligent soul was vivified by Spirit after Jesus' physical death, and then, after three days this same intelligent soul was united to the risen body.
Or, alternatively, if we understand "was made alive in spirit" with a lowercase letters, it cannot denote Logos, which is not to "be made alive", for being the very Principle of vivification Himself, and neither can it denote body, which lies in the sepulcher for three days, but the only solution is that what is made alive, the spirit, denotes the created intelligent soul of Logos, a part of the human nature adopted by Him. If so, then the principle through which the spirit is made alive is only implicit in this sentence and can imply either Logos, or the Holy Spirit, or both together, for both are the necessary Principles through whom the Father bestows life.
Thus, both alternatives are plausible and tenable, and theologically acceptable. However, objectively, at this stage of my preparation, I think that the second alternative is more precise, because the continuation of the passage says that Jesus, while His body was dead, went with His intelligent soul - called πνεύμα or spirit - to the other spirits (πνεύματα) of those people who died in ancient times, even during the deluge and Noah. Thus, the parallel usage of "spirit" in the immediate sequel must indicate that they denote the same ontological thing, the created human intelligent souls, and that those souls not only in case of Jesus, but also in case of other human beings, survive physical death, for indeed, both Jesus' and their bodies are dead, when Jesus' spirit (i.e. Logos with His created intelligent soul) communicates with those spirits (the human persons with intelligent souls) of people whose bodies were for many centuries dead.
Look one more important nuance: text says "He was put to death in body, but made alive in spirit" - those two verbs θανατωθεὶς ("was put to death") and ζωοποιηθεὶς ("was made alive") are used parallely expressing the same instance, so that it is not that He died and for few hours His spirit was also dead and then only it was made alive, but the very moment He died, His spirit was made alive. Now what does it mean? If, as we have established, the spirit most plausibly denotes God the Son's created intelligent soul, then we can assume that this soul was vivified by the very act of Christ's voluntary death, immediately before which He said "it is accomplished" (John 19:30), what is accomplished? The highest possible condition of this soul is achieved: for He loved in deed humanity with highest possible love, for there is no love higher than laying one's life for others. This highest condition that was achieved by death on the cross, could be called "vivification of soul" (to give just a dull analogy, if one sacrifices some of his money to a needed person, by this act he vivifies his own soul, turning it from the 'death' of stinginess, to the 'life' of generosity); otherwise, if we consider just continuation of existence after death, this continuation of existence also souls of disobedient sinners possess, to whom Jesus appeared in his truly living soul shining with divine grace while His body was yet laying in the sepulcher; yet, those sinful souls, while continuing to live, did not possess life in the deeper, more important and metaphorical sense - they were waiting for very long for this life to appear to them in the Person of Jesus, which was the greatest joy for them.
This teaching that intelligent souls survive bodies is a standard doctrine of the mainstream Christianity, for example, Catholics and Orthodox in ordinary liturgical cycle offer prayers for the alleviation of sins of the intelligent souls of the deceased Christians, and also ask the intercession to the intelligent souls of those saintly Christians - the saints, like Apostles, or martyrs etc. - who gained intense grace and became worthy of incredible closeness and boldness before God; in fact, remains of their bodies are venerated on earth with a reference to their living souls and intense prayful relationship with God. Thus, in the life of Church it is fundamental to believe that the intelligent soul does not die together with body, but continues to live, not though naturally, as in Platonism or Pythagoreanism, but through grace of God.