What is the history of atmospheric O₂ concentration?
Refer to the stratigraphic chart for timeline and stratigraphic units. And i tried to be as up to date as possible in the limited time. Which is also the reason why i omitted some details in favour of an overview.

It is assumed that during the early and middle Archaen only very sporadic oxygen production took place. This changes towards the end of the Archean, when a flow of oxygen from shallow ocean parts to the atmosphere began.

This article suggests that the following "great oxygenation event" (goe), at the early Proterozoic 2.33Gy just took up to 10 million years. During the goe, atmopsheric oxygen increased to 1 or 2 percent, the exact percentage seems unclear. But it seems that in some places, a fully oxygenated ocean existed slightly before the goe at the end of the Archean, at ~2.5Gy. These waters would have been able to produce excess oxygen for the atmosphere in a small or regional scale slightly earlier.

Atmospheric O2 stays low during the Proterozoic, probably because it is used up in weathering processes.

At the beginning of the Cambrian, O2 was still low (~5%). This article describes the development thorugh the Phanerozoic by combining data from modelling and proxies. See Figure 3 (there's your plot;-). It shows that not before the end of the Ordovician atmospheric O2 rises to above 10%, topping off at the end of the Permian at ~32%.

These days, oceanic as well as atmopsheric O2 levels are falling and will continue to do so because of fossil fuel combustion.