These are not counted in Story Mode, thus, any other game mode seems to work minus Training. Here is a list of levels you need to play:
XGard - Underground Prison
Avengers Tower - Lab
XGard - Bifrost Bridge
Knowmoon - Gravitron Core
XGard - Throne Room
New Metro City - Downtown
Avengers Tower - Briefing Room
A.I.M.Brella - Control Room
Dark Kingdom - Heart of Chaos
New Metro Ciy - Crossroads
Valkanda - Plains
Unknown - Training Chamber
Knowmoon - Walkway
A.I.M.Brella - Laboratory Pathway
Abel City - Sigma's Lab (Unlocked by Beating the Story Mode)
Dark Kingdom - Wastelands (Unlocked by Beating Story Mode)