Well, you've got enough heat sinks to move and fire, but 60 of these things...I'll say a mixed reinforced regiment against it. Plasma Rifles, infernos, for starters. LRM machines with mines, since your movement's pretty slow it's going to be hard to get around or through those fields. Without hardened armor, I'll go for maximum critseeking and golden BBs, plus bring a very large amount of infantry to the field. See above; you can pick away at them a few troopers at a time, but then you're ignoring the mechs shooting at you - or else you're shooting the mechs and letting the critseekers get close. Skip BA, they're REALLY screwed by your weapons profile - they take damage like regular machines, and there's a reason I call gauss rifles against BA 'Elemental Bowling.' Onboard Arrow IV if I can get it, mostly for laughs, if not then a lot of missile launchers for smoke rounds and fires.
You can't deal with excess heat, and getting hit by PRs and infernos is going to remove one of your ERPPCs from the table - though to be fair, there's very few mechs that DON'T have heat problems. Not really a critique there, but heat weapons are indeed a weakness, especially when you're losing 25% of your firepower to keep cool.
At 3/5/3, you've got decent maneuverability for a monster brick, but it's still slow - if I can get you in tight terrain, or simply deny access to hexes by mines and choking your cluster's movement, then I can force them into kill zones. Drop a dozen Archers, perhaps, denying movement through one area of the map, for example - you don't have anything faster to get over mines and become a movement threat.
Dictating range is a big thing - since all your force moves at the same speed, and is one of the lowest speeds in the game, a regiment of 4/6/4 or faster (and they get damn fast in the DA) is going to consistently provide targets that can keep at long range and keep up movement modifiers. Meanwhile the best you can put out is a +2 TMM for incoming fire, which means a lot is going to hit.
Critseeking is important, especially on those gauss rifles. Good job putting them in the arms - it means crits won't risk gutting torso locations and taking half your firepower. That said, they're still explosive, and you're not running Ferro-Lamellor armor. LBX, SRM barrages, and aforementioned infantry. If we're gonna get crazy with theoretical units, there's some absolutely bat-**** infantry units you can make under the rules that make regular rifle infantry look like hippie protestors with broke-down VWs. And with the way infantry does damage, and can reach out to range 15 with certain weapon types, foot infantry can be dangerous. Without anything to deal with meatbag infantry (see prior 'bowling' comment for battle armor) it's gonna take a while to grind them down using those big guns...and that means you're not using them on mechs.
Side note on those GRs - a crit on those is still an ammo explosion, which kicks two points to your pilot's head (or, if you've got autoeject going, punches out your pilot.) If I can crit both the GRs at some point you've got pilots that are risking sleeping off four pilot hits, and trying to wake up from it. That, plus engine crits for blowing your heat out of the water (all those delicious XLFE slots) limits your firepower or movement.
Artillery, again, kind of gets into the munchkinny bit, but it's one of those things that's still boardgame acceptable. Arrow IV, preferably, because there's a LOT of it in the game, and targeting hexes that I know you're gonna have to go through (see minefields, smoke) means splash damage out the wazoo. My intent is to deny access to some of the battlefield, and turn the rest into a killbox where you have to maneuver slowly to.
Now, those guns you have, on my 'Mechs, are going to be rough. I haven't bothered to do BV calculations, but 1/36 hits is going to be a headcap; with 180 of them firing (assuming I'm doing my job, and you're only using one ERPPC and two GRs because of heat)...well, if all 180 hit (they won't) that's five of my machines down every turn. Fortunately, at 3800BV each for your units, 228,000 BV of inner sphere mechs and infantry is going to last a while even at 5 deaths per turn.
Offhand, I'd also throw the ECM game in - you've got a targeting computer, which is good, but ECM bubbles and ghost targets will make hash of your gunfire, and you have no way to counter it with ECCM of your own. Beyond that, maybe some fast movers to tie up your shooters, provide targets with very high TMMs which maneuver to either get backshots on you or force you to turn your backs to my main gunline, which is still going to be heavily built around some holepunching and a truckload of critseeking, trying to grind down the guns you've got.
Battletech's really a game of combined arms; it's a fine example of the difference between a problem and a dilemma. A problem is some very large, powerful mechs with very big guns - a dilemma is a mixed force that can control a battlefield, deny terrain, block LOS with smoke, and be able to make big holes in armor as well as exploit them for crits. If you want a WWII comparison, the Astartes is the Yamato or the Maus tank...but ask history how those got taken down. It'd make a good centerpiece machine, but it's not a be-all end-all of combat, and has some serious weaknesses that need allies to supplement it. Just like the Hellstar, for that matter, or any other all-giant-gun Mech. Looking at you, Gausszilla...