Just for giggles, here's a Theraveda outline of the Four Noble Truths. Note the specificity of the First Noble Truth, which is typically shortened to "Life is suffering." (Words in all-caps are my emphasis.)
----- 1. The Nature of Suffering (or Dukkha): "This is the noble truth of suffering: birth is suffering, aging is suffering, illness is suffering, death is suffering; sorrow, lamentation, pain, grief and despair are suffering; union with what is displeasing is suffering; separation from what is pleasing is suffering; not to get what one wants is suffering; in brief, the five aggregates subject to CLINGING are suffering." 2. Suffering's Origin (Dukkha Samudaya): "This is the noble truth of the origin of suffering: it is this CRAVING which leads to renewed existence, accompanied by delight and lust, seeking delight here and there, that is, craving for sensual pleasures, craving for existence, craving for extermination." 3. Suffering's Cessation (Dukkha Nirodha): "This is the noble truth of the cessation of suffering: it is the remainderless fading away and cessation of that same CRAVING, the giving up and relinquishing of it, freedom from it, nonreliance on it." 4. The Path Leading to the Cessation of Suffering: (Dukkha Nirodha Gamini Patipada Magga) "This is the noble truth of the way leading to the cessation of suffering: it is the Noble Eightfold Path; that is, right view, right intention, right speech, right action, right livelihood, right effort, right mindfulness and right concentration." ----- "Clinging" and "craving" are roughly equivalent to "attachment" and "desire" in the context of MMY's teaching. Pleasure per se isn't suffering, IOW, it's craving it and clinging to it that results in suffering.