Place tomatillos, onion, garlic, and jalapeno peppers into a saucepan over medium heat, and pour in enough water to cover. Bring the mixture to a boil, reduce heat, and simmer until the tomatillos soften and change color from bright green to a yellow-green color, 5 to 8 minutes.
With a slotted spoon, transfer vegetables to a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the tomatillo mixture moving before leaving it on to puree. Puree until smooth, about 1 minute; mix in salt, cilantro, and lime juice. Blend again for a few seconds just to mix.
Scoop out the avocado flesh, and place into the blender; blend until well mixed. Adjust salt, cilantro, and lime juice before serving.
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