The Canton War and the 1883 Gyemi Coup
During the Canton War in 1850-1857, the Coreans fought alongside the Dutch. In 1883, the educated aristocrats of Corea overthrew the Tsjosan dynasty and formed the Sjakwang state, with the Ki family as the royal house.
The Qing state, now severely weakened by internal strife, did not like what was happening in Corea. They decide to intervene in the Corean situation. Believing that the Coreans had strayed further away from Qing influence, the Qing state decides to send whatever troops they had left and restore order in Corea, a rash and ill-fated decision that would cost them their entire empire. This marks the beginning of the Sino-Corean War.
Expectedly, the odds were not in the Qing's favor. The Qing once again requests their Dutch allies to intervene. This time, however, no Dutch reinforcements were coming to their aid. The Qing were alone in the fight against Corea.
It was later uncovered that Corea had secured a secret pact with the Dutch a year earlier and got them to promise not to intervene in any case of Qing aggression. Furthermore, the new Corean state had secured the support of the Russians. Russian and Dutch support fueled the Corean war effort. The war ended with the Treaty of Peking (1888), with Manchuria partitioned between Corea and the Russians. This led to the creation of Poeja, a Corean sister state in Manchuria.
The defeat at the hands of Corea completely rendered the Qing helpless, and the Qing's grasp on their western territories had waned. This triggered a race for territorial expansion between Russia (from the north) and the British Empire (from the south). This also led to a period of further increased Russian activity in East Asia and especially in Japan.