There are no differences between Easy difficulty and Legendary difficulty on The Armory.
You can waste time on this level by messing up the lights test, not looking at Master Guns right away for the shield test, not looking at him to trigger his closing dialogue, and not getting in the elevator right away.
The only strategy on this level is to push your allies. Pushing Master Guns to his location saves less than a second, but pushing Sgt. Johnson saves more time. Wait for him to finish walking out, then push him back into the elevator, near where he would walk back. This must be finished before Johnson finishes the line "Don't worry, I'll hold his hand." If you push him too early, he will continue trying to walk out of the elevator. Too late, and you will glitch his path finding, making him walk into corners and wasting time. Once you're done pushing, look at Master Guns to trigger his dialogue immediately.
If you get the famed "Chili Hole Skip" (Master Guns omits the line "so shut yer chili hole"), you save about a second.
When the elevator goes up and opens again, push him into the tram. You want him to start walking before you push, otherwise he will walk into the corner. You also want the dialogue "Earth... Haven't seen it in years" to trigger immediately, so stop pushing just before he gets to his spot. Otherwise he will spin around and look at you for a second.