A friend of mine plays beasts and I have developed some alternatives to magic and shooting if you either want to engage in or cannot avoid combat. A couple key items to keep in mind are that minos are expensive (especially with upgrades), start with frenzy only if a doombull or gorebull is with them and have poor AS and leadership. Keeping that in mind, here are a couple tactics that have worked for me:
1) Skrox - A standard block of 6 minos will run well over 300 points and closer to 400 if it has any upgrades or command. An equivalent point value of skrox can contain 3-4 krox, command and extra skinks beyond the minimum if only 3 krox are taken. A 3 krox unit deployed 10-12 across can advance, shoot and then S&S, dropping about 6 wounds of minos. In combat, the skinks strike first and will kill another mino on average, leaving the battle at 3 krox vs 3 minos, which will likely result in nearly equal wounds caused but exchanging skink wounds for minos wounds is a fantastic bargain. Even with impact hits, the minos are likely to lose combat since the skrox will still have 3 ranks & banner to start, resulting in a fleeing mino unit. Even if the skrox lose, they are steadfast and will finish the minos off the next turn.
2) Sacrificial lambs for the minostar - the minostar (18+ minos & mino characters) can be really nasty and rip through lizzie infantry with loads of S5/S7 attacks. To counter this, a suicide skink unit with a frontage of 1 can charge, lose combat and then the minostar is forced to pursue (albeit d6"). This can be used to pull them 90 degrees away from the main effort (requiring an entire turn to sort themselves back out) or to draw them into a trap. The trap is set by placing another disposable unit 1-2" away from the first so that the overrun hits it as well (leading to a 2nd overrun during the mino turn). Lizzie units are positioned to hit the flank(s) during their own ensuing turn with a block of infantry supported by steggies & characters. This should result in a combat win for lizzies and potential breaking of the minostar (unless it has the crown of command, which is likely). If the crown is in the unit, hitting one flank with a big skrox unit and the other with steggie &/or carnie lord & infantry block works well since it prevents combat reforms and thus the number of minos fighting every turn decreases as casualties are inflicted. Eventually, the unit can be ground down to nothing although this will take a fair bit of time or you may get lucky and have it fail a break check (lore of death with doom and darkness will really speed this process along!!).
3) Scar vet cowboy - for minos without g/w, the cowboy with dawnstone can hold them in place and likely win combat. If the minos don't break, another unit can flank them in a subsequent turn and then they will definitely break from static CR and active wounds inflicted.
you can even mess up his battle line by forcing the "minostar" to run sideways and block another units advance. just a word of caution though. if you do this, the minotaurs will start stacking their frenzy. you will pretty much never be able to fight it if you start doing this. "when you hold a tiger by the tail it is just as difficult to let go as it is to hold on" 