A majority of the achievements build around the campaign. I highly recommend simply playing through the campaign once on hard before going for the trickier campaign achievements. It will net you these four achievements, if not more:

Forest Menace
Encounter forest warriors in Campaign



First Encounter
Encounter aliens in Campaign



Conqueror
Complete Campaign



Napoleon
Complete Campaign on highest difficulty


Some levels can be very challenging, especially on hard. A lot depends on your strategy at the start of the round. If you get stuck, I would recommend watching YouTube videos of other people playing the same level - I think writing a guide on each level would be a pain to me and you.

Note: Most videos will be from the PlayStation version of the game, in which the levels are the same but in a different order. For best results, don't search for "mushroom wars level 17 hard", but rather include the name of the map, for example "mushroom wars veymarn hard".

Lightning
Complete Campaign in under 60 minutes


After having completed the campaign on hard and possibly having two hours, you might shudder whilst reading the description of this achievement. But don't worry, I'll explain why it isn't as hard as it looks: For each level, the timer on the top right counts the fastest you did in any level - no matter on which difficulty setting. So, I'd recommend starting from scratch and rushing the levels as fast as you can on easy. You won't take too long after having already played through the game on hard. As soon as your timer drops below 1 hour, you'll net the achievement.

You will have already noticed, that after each level you gain different rewards depending on your performance and play style. I'll quickly explain how to get each of them:


The achievements linked to the rewards are as follows:

Gatherer
Earn each reward at least once



Collector
Earn all 9 rewards in a single Campaign level



Perfectionist
Earn all rewards in all Campaign levels



There is absolutely no doubt that the Perfectionist achievement is the hardest achievement in the game - just in order to get the Strategian reward on all levels, you'll have to complete each level again on hard without losing a house and with 100% successful attacks. I can't comfort you a lot, at this point I am also still a long way from getting it.

Fighter
Win a Skirmish game



Veteran
Achieve victory on all Skirmish maps on highest difficulty



The first is a drive-by achievement, the second one requires you to finish each Skirmish map on hard. Again, I would highly recommend watching YouTube videos of people finishing levels if you're having trouble.
Also, try selecting Domination or King of the Hill as mode. They are often a lot easier than the norml mode and Domination can be won within seconds on some maps.

Spartan
Capture 300 enemy buildings


Self-explanatory. If you've already finished the campaign, you should have netted this whilst doing so, otherwise I'd recommend finishing a few Skirmish matches until you have it.



Escapee
Capture an enemy building without having any of your own


Also self-explanatory. Can be achieved in any campaign level by simply getting bashed by a normal or hard AI and then sending your last troops in an empty enemy village just before your last village is captured.



City Builder
Upgrade your village to level 5


In order to upgrade a village to level 5, you'll need to have 999 men in your village. Now, let's do some maths: The maximum capacity of a level 4 village is 80 men, that means you'll need 13 villages of your own, having the maximum possible amount of troops and all villages upgraded to level 4. This also means that you'll need a 14th village for your enemy, so that you don't directly win when capturing the 13th village.
You can use any map that meets these requirements, I used level 16 (Vituhburg) for this achievement. Mathroy suggests using the Duplex I Conquest map, which may be easier. I recommend doing it on easy, as no difficulty is required.



Leader
Achieve level 5 morale


Self-explanatory once you've encountered morale on level 11 (Veymarn). I recommend getting this achievement on the same level by simply defending your starting villages on hard.



Devastator
Achieve maximum attack level


This achievement requires you to reach 5 star morale whilst having four forges under your command.
I recommend getting this on hard difficulty on level 18 (Angaso), converting enough buildings until you have four forges and then letting the AI bash your defenses until you have 5 star morale.

I hope my guide helped you! If it did, please feel free to let me know in the comments or by simply rating/favoriting it. If something has remained unclear, you've found false information or feel my guide is missing something, please also let me know and I'll get to it as soon as possible.