Saying “all life is suffering” seems a gross misrepresentation of the First Noble Truth. Perhaps more helpfully, skillfully, wisely put: it is “the truth of suffering,” or even “all life contains suffering.” The words “suffering,” “stress” and even “unsatisfactoriness” don’t really seem totally and adequately translate “dukkha” either — “commonly explained as a derivation from Aryan terminology for an axle hole, referring to an axle hole which is not in the center and leads to a bumpy, uncomfortable ride.”
Another decent dukkha definiton is ‘made up of the prefix du and the root kha. Du means “bad” or “difficult”. Kha means “empty”‘ with one interpretation of this in the graphic below:
However, on an ultimate level, yes, until full awakening is realized, it seems all life is suffering — at least on the very subtle layers of craving/clinging to being/becoming and/or craving/clinging to non-being/non-becoming. Nearly all phenomena seem associated with this. For example, if getting up to walk to the bathroom, there’s craving to want to do bathroom stuff. If scratching, it’s likely there’s subtle craving to want to no longer be somebody with an itch. Crappy examples but perhaps enough to make the point.
These more subtle forms of dukkha are not so practical for purposes of everyday life though. More practical is acknowledging whatever suffering, stress, and/or unsatisfactoriness happens. And then how do we respond? Easy answer. With compassion. Compassion here mostly meaning simply to acknowledge, instead of not noticing or denial, with willingness to skillfully and wisely do what can be done for alleviation.
Enter Great Compassion, Mahākaruṇā, the ultimate compassion to aspire to:
“the meditation that Buddha continued throughout his life, the meditation practice that brought him to realization, is explained in the Surangama Sutra, and its results, in the Surangama Samadhi Sutra. In the Surangama Sutra it is explained by Avalokitasvara as being his practice, resulting in the perfection of mahākaruṇā.”
. . . Unlike karuṇā—compassion that must be developed—mahākaruṇā is the intrinsic naturing of all appearances, is Buddha-nature, and thus the Buddha naturally manifested this responsiveness in his every word and deed.
https://buddhism.stackexchange.com/questions/44969/what-was-the-name-of-the-great-compassion-meditation-the-buddha-did-for-a-signif/45015?noredirect=1#comment71868_45015
It’s also said the Buddha spent time daily practicing compassion:
The Last Watch ( 2.00 a.m. to 4.00 a.m.)
For the first hour the Buddha would walk up and down meditating and freeing himself from the discomfort of sitting all day. He then would sleep for an hour. Thus we can see the Buddha was busy the whole day. In fact he only slept one hour each day during this 45 years of teaching. During the early hours of the day he saw the whole universe, blessed it with his boundless love and brought happiness to millions.
The Buddha’s Daily Routine
What follows is more experimental involving mostly perception, reflection and contemplation. If not calling to you, or remain unmoved, please pass on it for the time being. Furthermore, any and all constructive critical responses are welcome — especially why this ought to be abandoned and/or any improvement suggestions.
The intent: how to continually practice karuṇā — compassion — at least in the background, even if/when life calls more for the other Bhramaviharas. Here’s how:
If metta (loving-kindness) is called for while doing compassion practice, particularly amongst everyday life, unless already completely, fully and totally enlightenment-realized, compassion is still helpful and needed. Mere acknowledgement — the primary type of compassion previously mentioned — also closely resembles loving-kindness, especially in light of all the other potential unskillful responses and ways of being, and not responding and being in the world. Plus, nearly any sort of true compassion is quite a kind occurrence.
For each and every incurring life instances where the unstoppable friendliness of metta is pertinent, but not occurring, this deserves our compassion as well. Like all those times strangers pass by each other with (seemingly mostly) unconscious, subtle but restrained ill-will — or even with indifference — require the compassion of knowing that this too stems from (unresolved) pain. At the same time, we are all doing the best we can, if we could do better we would.
Feeling needy about loving-kindness; not living up to expectations about loving-kindness; and clinging to loving-kindness warrants compassion too.
Knowing how to respond wisely in any moment — even in cases where the best response is no response, and/or giving someone extra space and alone time — is both lovingly-kind and compassionate.
Also, the level and degree of metta possible yet currently unavailable in this world warrants more compassion not less.
Compassion can relate to mudita — gladness and rejoicing, especially reveling and delighting in other’s well-being — by reflecting on all the times where more and more genuine joy can be so helpful. Exaltingly reflecting on the glorious compassion resulting from how authentic rejoicing helps lessen suffering overall and in the long run.
Perhaps another reason some beings act in such atrocious ways is because they falsely believe doing so will result in less pain and/or more mudita — rejoicing. Could such depravity continue if such beings already experienced all the joy their hearts desired? Probably not. Beneath this lack of joy much dukkha cries out for compassionate acknowledgment to release pain in order to know peace.
When life beckons for equanimity often times we need self-compassion. Again, the lack of full realization of awakening is still a form of dukkha calling out for the self-compassion of holding such challenges in the wisdom and balance of equanimity to the degree currently available.
Seen another way, (self-)compassion could underlie loving-kindness, vicarious joy, and equanimity because enough of a damn is given to realize even behind all phenomina — if not immediately apparent — there still likely remains subtle, latent tendencies of dukkha to be acknowledged along with the desire for dukkha deliverance equally shared with all sentient beings everywhere.
Furthermore, and perhaps somewhat ironically, throughly contemplating: “is there ever any logical, useful, helpful, wise, skillful, and/or wholesome (long-term) reason(s) for harming,” may help strengthen compassion.
Bonus: possbily the wisest, most elegant way yet of how the Bhramaviharas self-balance and interrelate:
The Four Sublime Abidings
Metta, [kindness] the love that connects, is an antidote to all forms of aversion.
It is not attachment.
If it slides into sentimentality, karuna [compassion] brings the heart back into balance.
Karuna, the love that responds, is an antidote to cruelty.
It is not pity.If it slides into sorrow, mudita [appreciative joy] brings the heart back into balance.
Mudita, the love that celebrates, is an antidote to envy.
It is not competitive.If it slides into agitated excitement, upekkha [equanimity] brings the heart back into balance.
Upekkha, the love that allows, is the antidote to partiality.
It is not indifference.If it slides into disconnection, metta brings the heart back into balance.
http://www.aucklandinsightmeditation.org/brahma-vihara/
Integrating Presence 
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