* Devil beater: silver + holy (burst) + evil outsider bane (or anarchic + lawful outsider bane).
* Demon beater: cold iron + holy (burst) + evil outsider bane (or axiomatic + chaotic outsider bane).
* Construct beater: adamantine + anarchic + construct bane (not a heck of a lot works well across the range of constructs).
* Lord of Blades beater / portal beater: adamantine + holy + construct bane.
* Xoriat Beater: byeshk + holy + enfeebling -OR- byeshk + wounding + enfeebling (lots of different combos available).
* Vermin beater - shocking (burst) + vermin bane.
* Giant beater: acid (burst) + giant bane.
* Ghost beater: ghost touch + holy.
* Skelly beater: holy + undead bane (blunt weapon).
* Undead beater: holy + undead bane (slashing) on maybe a silver weapon.
I've got my first TRs out there, and started crafting specialty beaters from pretty much lvl 3 on. The hardest to get are - of course - the special metal weapons (silver, cold iron, adamantine, etc.). It took me a while to find a cold iron kopesh for a reasonable price. I'll keep it in my inventory and upgrade the weapon as my TR gains in levels.
Note that by the time you start running Shroud, the things you need to make devil and demon beaters comes as drops from the Shroud.
Construct beaters are the hardest fo make as really the only good prefix on them that works across all constructs is Vicious. That attribute only only hurts you on every hit, but the animation is annoying as all sin. Anarchic hit Murats and a couple of others.
I was kinda surprised how well the Xoriat beater worked on Hound of Xoriat and in the Subteranne. My first-lfe pally, whose DPS was on the sucky side of "meh" at lvl 20 with the wounding / enfeebling went through outsiders and beholders like cr*p through a goose. Because he was a pure pally, he had the ability to break good DR anyways. My fighter has the first combo (holy + enfeebling).
Really, the only way to get purple numbers is to match an element on which some mobs are weak. In doing so, you're basically going to sacrifice another attribute somewhere in most circumstances. So what you really want to do is to basically break their DR, and have at least two "normal" numbers on each hit. If you can get double elemental damage after that, it's is like icing on the cake.
On some, like portal beaters and fighting elementals, they have DR that minimizes ALL damage. So, you're left matching cold weapons to fire elementals, and so on.