The waves progressively get more difficult, so the reason I split this up from the beat 25 wave achievement is because the method of beating waves needs to "evolve" or change from what you were able to get away with in the first 25 waves.
For starters, on waves 25-40, you will want to continue to upgrade and employ the strategy of spamming farmer units whenever you can in order to stall the enemies. In addition, I recommend continuing to upgrade your bow/bow allies in order to get some good range on enemies as farmers slow them down. In the later waves, you will notice a plethora of enemies sitting in the backfield that are ranging you, and even healing the zombies. To deal with them, use the Lethargy power up to slow the enemies in front, run through them, and quickly deal with the low health problem zombies sitting in the backfield with your second power, preferably Katana Slash.
Once you reach wave 40 you will unlock the "Troop Trample" powerup, also sometimes referred to as "Katana Wave". Once this is unlocked, you will want to immediately start utilizing this power up, and level it up. I recommend replacing Katana Slash with this and keeping Lethargy to slow the enemies. Continue to spam farmers as you can and then deal with the troops in the same way as waves 25-40. Continue to utilize Lethargy, and utilize your new power Troop Trample, to make quick work of the enemies. The later levels get tough, but using this strategy should help a lot.
Once you reach the last wave, level 50, you will face off against a boss, so see the "So Long" description below on how to deal with that zombie.