1. Respiratory alkalosis, as you know, means high extra-cellular pH as a result of ventilating off too much CO2, a la the Henderson-Hasselbach equation where pH = bicarbonate concentration divided by PCO2, i.e., pH = [HCO3]/PCO2).  Reducing the PCO2 obviously means an increase in the value of the pH.

2. Low PCO2 as a result of over breathing means less CO2 diffuses into red blood cells. 

3. Intracellular red blood cell pH rises because less carbonic acid is formed. 

4. Less CO2 and increased pH in the red blood cell lead to a change in the conformation of hemoglobin, wherein hemoglobin becomes less inclined to give up its O2 (Bohr Effect) to the plasma.

5. The same changes in the conformation of hemoglobin means that less nitric oxide is released into the plasma, the key player in vasodilation (and constriction). 

6. The reduction of nitric oxide, along with the effects of CO2 deficit on smooth muscle function, means vascular constriction and greatly reduced blood supply to tissues that need it. 

7. The combination of hemoglobin's higher affinity for O2 and significantly reduced blood flow translates into much less oxygen and glucose for cells that require them.

8. During cell metabolism, one glucose molecule results in 38 ATP molecules, the molecules the cells break down for their energy.  When cells don't get enough O2 they move into anaerobic metabolism, where ATP molecules are generated in the absence of adequate O2.  This process, however, is about 5% as efficient as aerobic metabolism, wherein only two molecules of ATP are generated.

9. In the cytoplasm of cells, glucose is broken down into pyruvic acid and generates 2 ATP molecules before entering the mitochondria.  In the absence of O2, however, the pyruvic acid does not enter the Krebs Cycle in the mitochondria, but instead ferments and forms lactic acid.  The cell thus moves into lactic (metabolic) acidosis.

10. The lactic acid is buffered by bicarbonates and is later reconfigured as glucose once again (gluconeogenesis) or is oxidized into water and CO2.  This process is called "utilization."  When utilization is slower than the production of lactic acid, it accumulates and you begin to suffer metabolic acidosis (in this case lactic acidosis).

11. Thus over breathing results in extracellular alkalosis leading to intracellular acidosis (as a result of vascular constriction combined with the Bohr Effect).