Well, like the scene I referenced was the climax of the movie, going head to head with Mechs, Tanks, or Battlearmor when you're PBI should be the climax of an entire campaign. If you die (likely, when one hit will red-mist you), then it was after having had a 'good run' in the campaign. Even then, you're not actually killing anything. Like in the scene, a major victory was just in using grease-laden socks to attach explosives to the tank's running gear. The resulting explosion didn't actually damage the tank, but it did snap a tread.. thus 'mobility killing' it and ultimately stopping it from crossing the bridge.
Unless you have your own armored assets in the party, that's the only sort of victory one can expect to have.
That being said, there are a few, very few, examples of successful unarmored infantry units/characters taking on and beating armored targets. I'll reference you to the exploits of Cassie Suthorn (of 17th Recon fame) and those of the Black Cats mercenary company. Basically, what they show as possible is setting up booby-traps, and then luring the armored targets into them. (tank won't do much after it falls into a pit, etc)
Dovetailing on what guardianashi said about special weapons and tactics, remember that there IS such a thing in the BattleTech universe as "anti-mech trained" infantry.
They use grappling rods to climb up a hostile mech, place satchel charges at strategic points, and GTFO before the mech kills them. Even under the best of circumstances, the mech will probably kill a bunch of them, but since they come a platoon at a time, the idea is most will get away. Kind of works, just not for those unlucky enough to be swatted. It translates to ATOW RPG play, just not very well unless you have enough NPCs to fill out a platoon to soak those stray deaths.