This is a printable checklist of all of the required units for the Model of a Modern Major-General achievement. I haven't confirmed if the spaceship parts are also required, you may need to build those as well.
For the achievement, units must be trained, not purchased, gifted, or upgraded. So upgrading your warrior to a swordsman will not count as training a swordsman.
Model of a Modern Major-General Checklist 2016-10-05
Model of a Modern Major-General Checklist