There are two problems with the argument that "no one would die for a lie, so the apostles' witness unto death for Christ's bodily resurrection must be true" (comment on previous post). As much as I would like to believe this argument, it rests on uncertain historical foundations, and so I think we should be cautious about employing it in apologetics.
The first problem is there is uncertainty from a strictly historical point of view as to whether all the apostles were in fact murdered as Christians. According to tradition, they were all murdered as Christians, except for John who is said to have died of old age.
The second problem is that, even if it could be proved that some of the apostles were murdered as Christians, it is unclear that they died as martyrs in the technical sense, that is, as witnesses in a criminal trial before a magistrate after being given a chance to renounce Christ to save their lives.
As to the first problem, Candida Moss makes a compelling case that the vast majority of the stories about the murders/martyrdoms of the apostles are apocryphal or legendary, mostly coming from the late second through sixth centuries. She points out that these apocryphal accounts "are filled with stylized and fanciful narratives of talking animals, resurrected smoked fish, and flying magicians. Whoever wrote them never so much as met an apostle, let alone witnessed his death" (The Myth of Persecution, p. 137). I think she is right to be skeptical of many of these traditions.
Of all the apostolic deaths, the ones with the strongest weight of ecclesiastical tradition are the deaths of Peter and Paul. Both are reputed to have perished under the Neronic persecution after the Great Fire in AD 64. That Peter, at least, was murdered as a Christian during that persecution I take to be very probable. However, the details of the circumstances of his murder are murky at best. The earliest account of the death of Peter is found in The Acts of Peter. It is part of the so-called New Testament apocrypha and was written in the second half of the second century. It is from this book that we get the tradition that Peter was crucified upside down. But it is also from this book that we get fanciful accounts of "resurrected smoked fish, and flying magicians." So it is hard to know how to separate the kernels of historical fact from the chaff of legend. As for Paul, we know very little about the circumstances of his death, but given that he was under Roman custody as a known Christian, we can speculate that he probably did in fact die as a martyr. Ignatius (ca. AD 110) refers to him as a martyr (Letter to the Ephesians, ch. XII) but we can't be certain he is using the word "martyr" in the technical sense, and he gives no additional details. Unfortunately, we just don't know exactly how Paul died.
As to the second problem, even when we can narrow down the list of martyrdom stories to the most historically verifiable, we don't know if they died as "martyrs" in the technical sense, that is, if they had the opportunity to renounce Christ and live. For example, we know that at least one of the original twelve, James (one of the sons of Zebedee), was killed by Herod Agrippa (Acts 12:2). This is the only one of the twelve whose murder is explicitly narrated in the Bible. However, the text never says that he was given an opportunity to save his life by renouncing Christ. It looks more like he was simply arrested by Herod and executed to please the Jewish leadership.
Outside of the twelve, we have the murders of Stephen (Acts 7) and of James, the brother of Jesus and leader of the Jerusalem church (aka "James the Just"), who was stoned to death by the Sanhedrin in AD 62 (Josephus, Antiquities XX.9). But, again, in both instances, they were simply put to death -- and by the Jews, not by the Romans. There was no opportunity for them to renounce Christ in order to be spared. So while they were murdered as Christians, they were not martyrs in the technical sense.
The technical martyr scenario occurred later during the Roman persecutions at the beginning of the second century. This is the scenario of a Christian who has been denounced as a member of the "superstition" known as Christianity to the Roman authorities, has been arrested, and is now standing before a Roman magistrate and is being interrogated. The magistrate asks if he or she is a Christian repeatedly. The magistrate tries to give them a chance to renounce Christ and save their life. See Trajan's instructions to Pliny (AD 112): "Whoever denies that he is a Christian and really proves it--that is, by worshiping our gods--even though he was under suspicion in the past, shall obtain pardon through repentance." Only if the person stubbornly persists in proclaiming that they are a Christian are they then executed. Compare what appears to be something akin to a transcript of the interrogation of Justin Martyr and his companions (ca. AD 165).
The bottom line is that we have little solid historical information about the deaths of most of the apostles. With regard to one of the apostles (James the son of Zebedee) and with regard to an additional two early Christian leaders (but not apostles - Stephen and James the Just), we can say that they were murdered as Christians but not as martyrs in the technical sense. In the cases of Peter and Paul, it is possible that they were both martyrs in the technical sense. Tradition says they were, but we can't be sure.
Returning to the use of the apostolic martyrdoms as an apologetic argument, I think we should be cautious just because the historical evidence is so murky. I am willing to accept the ecclesiastical tradition that says that Peter and Paul died as martyrs. But not everything that I as a Christian have inherited from the Christian tradition is useful or wise to employ in an apologetic context. I would also add that, while I believe that Peter and Paul were murdered as Christians, I have doubts about whether they were martyrs in the sense of persevering in their profession of faith in Christ in spite of being given a chance to renounce Christ. The evidence suggests that they probably perished in the midst of Nero's attempt to use the Christians as scapegoats for the Great Fire in Rome in AD 64. This seems different from the scenario that we see in the Trajan-Pliny correspondence or the interrogation of Justin and his companions. It is probably anachronistic to read that technical "martyr" scenario (namely, a Christian standing for a Roman magistrate and being asked if he or she is a Christian on pain of death) into the first century. However, that is not to say the technical scenario could not have happened in the first century. Perhaps it did happen in the case of Peter and Paul. I just wouldn't stake my apologetics on it.