How is Ukraine going to win the war without defeating the Russian army in a large battle?

Short answer: Ukraine doesn’t need to win a decisive battle against Russia in a large battle.

Long answer: OK, buckle up, put on your thinking cap, and be sure to keep all arms and legs inside the car for this answer.

I think you misunderstand the wars that Ukraine and Russia are fighting. Each country has wildly different goals, and each of these goals requires different methods.

For Russia, the goal is simple: to integrate Ukraine into Russia as it was integrated into the Soviet Union. This is a part of Putin’s clear plan to reassemble as much of the former Soviet Union as possible. If the attempt to conquer Ukraine succeeds, it will probably embolden Russia to move on to the next former Republic of the late, unlamented USSR, such as Putin’s close ally Belarus, or Georgia, or Kazakhstan. Note that, of the former Soviet Republics, the ones with the greatest petroleum resources are Kazakhstan, Azerbaijan, Turkmenistan, and Uzbekistan. Note, also, that Ukraine has rich oil and natural gas fields in its eastern regions as well.

For Ukraine, the goal is simpler: to remain an independent nation, preferably without ceding any territory to Russia.

For Russia to conquer Ukraine, they need to suppress all resistance. This will likely require killing hundreds of thousands of Ukrainian citizens, destroying much of Ukraine’s infrastructure, and snuffing out what will certainly be a long, brutal, and expensive resistance. None of that will be even close to easy, and all of which will risk widening the war, potentially bringing in NATO allies. The very last thing Russia wants is to see either its forces routed by far-superior NATO forces, including US ones- remember that much of US military doctrine, to this day, was designed to fight a near-peer nation like Russia, not a long resistance like Afghanistan or Vietnam.

As for what it will take for Ukraine to win, that’s as simple as its goal: all they need to do is to make Russia decide that they’re too difficult of a treat to swallow. All they need is to not lose. As long as the idea of an independent Ukraine exists, people can and will be willing to fight for that idea. And, as long as the Ukrainian people are willing to fight against an invader that is unpopular on the national stage, they’ll have international support, such as from the US and other NATO countries, to do so.

Like the Afghanis or Vietnamese, the Ukrainians don’t have to slaughter every member of the invading forces. Heck, ideally they can capture more Russians peacefully and turn them into allies as they’ve already done. All the Ukrainian forces need, just like the Afghan fighters, North Vietnam Army, or Viet Cong, is to not be wiped out, and pick off enough foreigners that the invaders just give up. In all of the above cases, the US and USSR didn’t lose. That’s right, the US didn’t lose the Vietnam War, nor did the US or USSR lose in their the invasions of Afghanistan. The problem was, in all of the above cases, they couldn’t possibly win.