Tom establishes the "badass" in his Badass Bookworm by being the first character to beat a skitter hand-to-hand onscreen.
In "Grace", Pope kills a nest of sleeping Skitters by attaching a couple of grenades to a gas can and tossing it at them.
Anne kills the captive Skitter with nothing but a scalpel by reaching into its mouth and stabbing it in its weak point (the soft palate between the mouth and its brain).
"I might not be able to stop this, but I won't be a part of it!"
Pope may be a complete bastard but when he figured out how to kill the Mechs, with the help of Matt, and was demonstrating it to the 2nd Mass, this trooper was cheering along with the crowd.
Even after the attack on the alien structure fails, Tom still manages to strike a blow against the invaders by hitting one of the alien fighter craft with a Mech metal-enhanced RPG (basically a one-in-a-million shot), which then crashes into the structure and causes extensive damage to one wing of the structure.
Weaver: "Good shot."
In second season premiere, Mason is confronted by one of the Overlords and its Breaking Speech cherry picking of human history to claim that mankind is despicable. His answer? Punch the guard, take its stun rod, and use it on the Overlord.
Tom handing Pope a thorough ass kicking, for taking a compass from a dead member of the Mass (Jimmy). Multiple people note he nearly killed Pope, with his bare hands.
Pope telling Manchester what he really thinks of Tom, all while sipping some wine.
Pope: Tom Mason is a pompous, semi-erudite history buff, with delusions of grandeur.
Which is quickly followed by him telling Manchester to take his offer and shove it, because if anyone's going to take Tom down, it's going to behim, not "some tin-pot dictator in Charleston".
Tom beating the Overlord to death.
Which is only enabled by the Big Damn Heroes moment supplied by Red Eye's rebel Skitters.
When Karen electrocutes Captain Weaver, he screams in pain... and then asks "Is that all you got?"