Written by Sean McDowell whose dissertation research is focused on this subject.
While we can have more confidence in the martyrdoms of apostles such as Peter, Paul and James the brother of John (and probably Thomas and Andrew), there is much less evidence for many of the others (such as Matthias and James, son of Alphaeus). This evidence is late and filled with legendary accretion. This may come as a disappointment to some, but for the sake of the resurrection argument, it is not critical that we demonstrate that all of them died as martyrs. What is critical is their willingness to suffer for their faith and the lack of a contrary story that any of them recanted.
via Did the Apostles Really Die as Martyrs for their Faith? at The Poached Egg (Ratio Christi).