The easiest way is very simple , actually. If you are struggling with the campaign , just remember that quick stack spamming with mediocre units (samurai archers and naginatas) is the best way to go. Because the goal is to capture rather than to hold 40 provinces within the allocated timeframe , it is best to quickly research samurai units (the cheaper and more resilient the better). While you do this , recruit ashigaru yaris and bowmen to hold rather than to push border clans. By turn 10, you should already have enough samurai to go on the offensive.
Now the only tactic you have to employ is spamming stacks of bow samurai with a few units of naginatas at castles. To make things quicker , autoresolve any battles that only have garrison units as your losses will amount to something like 0-5 in those autoresolved battles.
When you capture a province , convert it to your religion immediately and garrison no more than 5 units (3 when you rebuild the castle). Just remember that autoresolving battles always destroys the castle.
After you capture a province ; rapidly move to an adjacent province to keep your enemy from recovering. You should have most of japan by turn 50.
On a side note do not neglect your navy (build it bigger) or you might have a nasty surprise invading behind your conquered lines.