In order to unlock Imagawa you have to beat all the lead engineers before they can get into your fort. If they even take a single step inside your fort you will not be able to get Imagawa.
The lead engineers will not come until a few minutes into the mission, When Shingen says "Implement the secret weapon" that is when they will star to appear. When they do start to appear you need to focus all your attention on killing them only.
If you need to find where they are located just press start and look for them in the officers section. After the first 4 come they will star to come in pairs. There are 8 lead engineers altogether and you will get a confirmation when you beat them all. After that complete the mission and you will get Imagawa
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