A travel distance of 11.500 kilometers in 9 days covered by flying surely requires a lot of energy.
If cells are fermenting, the ATP (energy) they generate only comes from glycolysis, which produces 2 ATP molecules.
If they are using aerobic respiration, glucose is completely oxidized to CO₂ through glycolysis and the Citric Acid Cycle, and the electrons enter the electron transport chain to finally reduce oxygen into water. In the complete process, up to 36 ATP molecules are produced.
In sum, aerobic respiration is much more efficient to generate energy than fermentation, so it's probably the main metabolism of the flight muscles in bar-tailed godwits.
Oxidative phosphorylation is a process that occur during aerobic respiration and this take place in the mitochondrial , is the process in which ATP is formed from the transfer of electrons from NADH and FADH2 through electron transport chain to oxygen, which is reduced to water.