How do you change ''he marched off to class like a soldier on a mission to a metaphor?

Well, "He marched off to class like a soldier on a mission," is a metaphor. It just happens to be a simile too.

Here's the thing: all similes are metaphors, but not all metaphors are similes. Both are comparisons made between dissimilar things; a simile just does it using "like" or "as."

If you wish to keep it a metaphor but make it no longer a simile, remove the like and insert a comma: "He marched off to class, a soldier on a mission."