Peter’s martyrdom is predicted in the gospels, as mentioned above, of course. It’s also recorded in the Acts of Peter (aka the
Actus Vercellenses.). Maybe dates to the second half of the second century?
The martyrdom of St. James Major is recorded in Acts 12:1-2. (Second half of first century.)
The Martyrdom of St. James Minor was recorded in Josephus (
Antiquities of the Jews), Eusebius (
Historia Ecclesiastica), and Jerome (
Lives of Illustrious Men).
The Acts of Thomas (
Acta Thomae) include his martyrdom narrative. It’s an early 3rd c. text, as far as I can tell.
The Acts of Andrew (
Acta Andreae) is referenced in a 3rd c. work, but scholarship believes that it was originally composed mid-2nd c., and includes his martyrdom narrative.
St. Matthew’s martyrdom was recorded in Eusebius (
Historia Ecclesiastica).
St. Philip’s martyrdom was recorded in-- yep, you guessed it-- the
Acts of Philip, which was written about the same time as Eusebius.
I’m having trouble running down an early-dated document recording the martyrdoms of St. Simon and St. Jude/Thaddeus. And St. Bartholomew has two different traditions surrounding his martyrdom.
And of course, there are later-dated martyrologies (Usuard, Bede, Florus of Lyon, etc) and other histories (Isidore, for example).
It’s pretty easy to make an argument that it was a common belief in the first century or two in the early Christian community. If you’re looking for something in the form of King Misdai’s diary, where he writes, “Dear Diary, today I had Thomas the Apostle executed”, you’re not going to find it.

But if you’re looking at it from the perspective that you don’t find any writings refuting various martyrdom narratives as being false accounts, that’s should be sufficient enough for a scholarly approach.
Are there seriously any credible early Christian historians who would argue that the apostles-- minus John and Judas Iscariot-- didn’t die for their faith?
