Encounter (browser, Flash) is a bite-sized puzzle/RPG with a whole bunch of depth to its simple-seeming gameplay. Japanese only, though the rules are largely intuitive.
I haven’t necessarily figured out all the nuances here, but note that there appears to be no maximum HP value despite the bar graph’s suggestion to the contrary. Success is definitely dependent upon raising your health far above the initial value.
Also of note: the powers in the upper-right corner are clickable and do not use up a turn. The powers along the bottom are passive traits, defining special results of matching certain types of figures.