LBX autocannons, and inferno SRMs on FAST platforms. you need at least 2 SRM infernoes for the really juicy crits, thanks to changes to TW, and you're going to have problems if he figures out the optimal way to run tanks in TW (finda good parking space, park, and shoot. don't bother trying to move, it's counterproductive after that first motive system crit.)
plasma rifles are also good.
Basically your guy is running customs, so use customs optimized for killing conventional units. That tends to mean lots of crit-seeking goodness and secondary effects weapons. things to avoid: Anything that jams, and builds optimized for killing 'mechs (Icebox energy boat builds).
it's a shame so many f what used to be legal aren't available now in terms of basic rules-the old inferno rules really forced a different kind of engagement, since a Com-2D commando could kill an Alacorn outright or force it out of position easily just by popping up with some racks of inferno munitions. (old rule that no longer applies; if your tank is in a hex and was hit by, or near-missed by, an Inferno SRM, he had to make a survival roll during the heat phase or die, and if he STAYED there, he had to do it again with a penalty. this kind of made parking with tanks a REALLY BAD IDEA. the change to TW's rules for infernoes have made it THE BEST IDEA EVER when running tanks. likewise, moving the artillery to the optional rules means camping up 2 to a hex is now THE BEST IDEA EVAR for tanks that park, esp. since Swarm LRMs are no longer a thing.)
but while most of the 'cheap' ways that 'mech units killed tanks have been removed from the game, and the crit table's been expanded to 'mech duration rolling contests, crit-seeking still works, just not that often. LBXs', large racks of SRMs, large racks of LRMs, plasma rifles, inferno missiles, these still work, and since his tracks are moving 4/6 at the start, that means they're not the total slab of armor they could be at 3/5, you just need to have something faster enough to provoke difficult targeting, that employs every cheap way left in the game to exploit his decision to use tanks in groups. Notably, crit-seekers are your very bestest friends ever, because if he's optimized himself at 4/6, you're still going to waste a lot of time eroding armor plate before getting to the juicy innards. massed cluster rolls will help here, you want things like the LBX Enfield 'mech if you can get it, or just turn out a custom with the same basic layout, backed up by archers and catapults to rain down the LRM fire en-masse as he makes his approach-force HIM to play aggressively, move just enough to get a TMM without the jumping penalty or running penalty, fire, move next turn, fire. rain down clusters of crit-seekers (LRMs are teh easiest go-to for this), then dust him with MORE crit seeking goodness as the range closes with LBX autocannons, then deliver fire with plasma and inferno at closer ranges.
it does mean more dice rolling. I recommend building a dice-box to handle groups of location/to hit data to speed up fire-phases, and have your movement pre-planned in advance with at least two options; won initiative, and lost initiative.
a few options you might consider:
Cavalry AH vtols for support, or any fast moving, SRM or LRM armed VTOL units to supplement or compliment the mechs on your team. alternately, fast moving light 'mechs that can build a high to-hit number like the venerable Jenner, able to bring cluster/critty weapons into range and maybe survive the experience. Alternately push for higher BV games that let you run heavier 'mechs that can weather the papercuts and get in close, where kiks, stomps, and axes can be brought into play, or shift venues from open terrain, to urban terrain and introduce him to the joys of rubble, building collapses and blocking roads. (Terrain that is impassable to vees, even tracks, can be created and used by 'mechs, urban tightens sight-lines and reduces the effect and impact of his massed LRM fire, and so on.)