Note; here is a tentative proposal for discussion. I suggest that chapter 1 and chapter 4 are trying to get Timothy to go to see Paul in prison, something he is reluctant to do.
A. Don’t be ashamed of the gospel or Paul 1:1-18
B. Endure hardship 2:1-14
C. Focus on sound exposition of scripture 2:15-26
D. False teachers will arise 3:1-9
B’. Paul endured and was delivered 3:10-12
C’. Focus on sound exposition of scripture 3:13-17
D’. False teachers will arise 4:1-8
A’. Visit Paul in prison who is about to be executed 4:9-22