The Battle of Khalkhin Gol or the Nomonhan Incident (depending on who you ask) is, of course, only the finale and largest engagement of the more widespread Soviet-Japanese border war that marked the clash between the Japanese and Russian imperial peripheries in northeast Asia. The wider conflict can in turn be tied to the Imperial Japanese Army's own fear of and a desire for war with the Soviet Union. In that sense, the primary goal of the Japanese in choosing to escalate was out of an effort to show strength and--at Nomonhan in particular--potentially to avenge a perceived humiliation from previous incidents on the border.

To give context, when Japan defeated Russia in 1905, Japan had secured control of the South Manchuria Railway, which ran from Changchun to Dalian. However, the Russian Empire maintained control of the Trans-Manchurian Railway, which linked Chita and Vladivostok by cutting through Manchuria, rather than having to go around the edge of Manchuria like the Trans-Siberian Railway. The Soviet Union maintained control of the Trans-Manchurian Railway following the Bolshevik victory in the Russian Civil War, and even fought a short conflict with Zhang Xueliang (the ruler of the Fengtian Clique which occupied Manchuria) in 1929 over control of the railway. When the Japanese seized Manchuria in 1931, there was some concern over whether the Soviet Union would take the opportunity to seize northern Manchuria, but--ultimately--the Soviets did not intervene as the Japanese moved into northern Manchuria. In 1935, the Soviets would sell their rights in the Trans-Manchurian Railway to the new puppet state of Manchukuo. All of this is to say that--in the inter war period--Manchuria was in many ways a disputed territory, with a strong legacy of Russian influence. In many places, the boundary between Manchukuo and the Soviet Union were poorly defined, with both the Japanese and Soviets having different interpretations of previous agreements resulting in any number of border disputes between the two. To give an example, the border between the Russian and Chinese Empires had been set with the Treaties of Aigun (1858) and Peking (1860), which held that the border between the two ran down the center of the navigable channel of the Amur River. Islands south of the channel would be Qing and to the north would be Russia. However, over the course of time, the channel of the Amur shifted, such that some islands which had previously been on the Russian side of the river were now on the Manchukuoan side. Disputes over these islands led to the Amur River Incident in 1937, a few days before the Marco Polo Bridge Incident kick started the Second Sino-Japanese War.

Adding on to this is that--throughout the 1920s and 1930s--the Imperial Japanese Army viewed the Soviet Union as the single greatest threat to Japan, and was focused on preparing for war with the Soviets. General Araki Sadao, the War Minister from 1931-1934 was particular forceful in his support for the idea of war with the Soviet Union, the first stage of which was to be the occupation of Manchuria. While Sadao was forced into retirement following the abortive coup of the February 26 Incident, many of the officers who supported him were transferred to Manchuria, where they carried their own beliefs about the Soviet threat with them. I've written previously on that aspect and gone into more detail on the Soviet-Japanese border clashes here, but--to summarise--the Kwantung Army--Japan's primary field army in Manchuria--were very concerned that any Soviet 'incursions' onto territory that--to Japanese interpretations--was part of Manchukuo were efforts by the Soviets to test Japanese defences in Manchuria, potentially in preparation for a full scale war. In that respect, the Kwantung Army -felt that every potential incursion must be met with maximum force, lest the Soviets see it as a sign of weakness. However, while the Kwantung Army saw these conflicts as challenges that needed to be met and addressed with force, the Army General Staff in Tokyo were much more concerned by the prospect of a border conflict escalating, dragging Japan into a war with the Soviet Union while the majority of the Japanese army was committed in China. In that respect, there were increasing efforts from Tokyo to moderate the activity of the Kwantung Army, efforts which the Kwantung Army pushed back against what was seen as interference from the central government.

Ultimately, it's less a question of what the Japanese sought to achieve but rather what the Kwantung Army--who had always had an independent streak--sought to achieve. By meeting perceived Soviet incursions in strength, they would prevent any Soviet belief in Japanese weakness.

I hope this has helped answer your question, and feel free to ask any follow ups!