One possibility is to heat the surface. This is "comparatively" easy since the bad guys could for example deploy an enormous solar sail (the term is apparently mega-statite) and use it to cook off the planet. It would double up as an extermination weapon, rendering the surface uninhabitable.
Exciting and focusing some kind of coronal mass ejection to the extent of stripping the atmosphere away is also efficient, provided these Berserkers - or Amadiros? - have the technology to pull it off. It would probably be difficult to strip off all of the atmosphere in a single go, but nobody says that once overwhelmed the system's defenses - they should do that in any case - they can't install themselves near the sun and start taking pot shots at the planet. This is the strategy preferred by the Ekhat of The Course of Empire.
Another relatively low tech possibility, with the advantage of being very hard to defend against and the disadvantage of only working against oxygen-nitrogen atmospheres (and requiring terrifying resources), could be to bombard the planet with magnesium pellets. The problem is of course to procure the magnesium in the first place: that much metal (the mass of Earth atmosphere is 5.1480×1018 kg) would be equivalent to almost a tenth of the maximum estimated mass for the Chicxulub impactor.
The DoomFleet would need to mine magnesium from somewhere and bring it along from system to system. Then the reservoirs could be placed in space in such positions and with carefully adjusted speeds to hit on the victim planet from all directions, at the same time.
The first pellets would burn violently in oxygen, forming magnesium oxide powder and raising the atmosphere's temperature enough to allow further reaction of magnesium with nitrogen (actually this wouldn't even be needed - the reentry heat would suffice to that). The resulting magnesium nitride is solid, but it would quickly react with water vapour from the now boiling surface of the oceans to form magnesium hydroxyde and ammonia, which would mostly dissolve in the remaining water while the dissolved oxygen would get outgassed (completely depleting the oceanic oxygen would take a long time). A large part of the available oxygen would be consumed by the fires engulfing the planet, though - forests, cities, all kinds of organic matter.
After a comparatively short time, the atmosphere would be replaced by a boiling fog of low-pressure water vapour and ammonia, and the planet would see its albedo significantly increased. I expect this to lead to a rapid cooling of the atmosphere (and the surface). After that, without the greenhouse effect from the atmosphere, the surface cools down to about -18 °C and we are left with a very thin, sterile atmosphere - carbon dioxide, ammonia, nitrogen, water vapour, argon - on a frozen surface. The remaining organic matter would capture what little oxygen still seeped from the oceans.
It's unlikely that any life form could survive the firestorms, the nuclear winter, the change in the environment and the subsequent onslaught of UV radiation after the disappearance of an ozone layer.
However, a more efficient way of destroying the planet would be to let the atmosphere alone (directly) and locate instead a suitable asteroid (or more than one) to deorbit and smash into the target homeworld. It would take the same energy as to move a comparable mass of magnesium metal. This is the preferred tactics of the Achuultani of Empire from the Ashes.
Now that I've thought on this a little more, so large a quantity of almost anything arriving at several kilometers per second would either burn in the atmosphere or contribute to its heating by friction, and make the planet uninhabitable no matter what.