If Diabride, Natural Pyroxenecrushes 2 of the opponent's Life Cloth and the opponent's Arc Aura's Life Burst is activated, both Diabride and Arc Aura will activate at the same time. In this case, the turn player's (the attacking player's) abilities resolve first - Diabride will up herself, and then put back down by Arc Aura's Life Burst.
To damage the opponent means to crush 1 of their Life Cloth, and if they have 0 Life Cloth when this happens, you win the game.
The second [Constant] ability of Diabride, Natural Pyroxene is triggered once per turn, and does not affect other Diabride. For example, if your opponent uses Don't Move and chooses two Diabride, both Diabride deal damage to the opponent (crushing a total of two times).
If you use Dark Matter while Diabride, Natural Pyroxene is on your opponent's side of the field, Dark Matter will add a Life Cloth, then Diabride's second [Constant] will crush that same Life Cloth. If you have 0 Life Cloth at the time Dark Matter was used, you will not lose the game, as Dark Matter resolves before Diabride.