Pretty straightforward, simply complete every level in the campaign. However, warning that resetting a level will require you to complete it again to get credit and sometimes it can bug out and not give you credit anyways, forcing you to do it all over again. I would advise not resetting any levels until you have this achievement.
This is the general strategy I use to complete almost every level:
1. Recruit young dwarves up to your pop cap and train workers and diggers until you have 2 of each (starting number varies by level).
2. Dig around all the fertile dirt blocks until you have uncovered at least 10-12 of them.
3. Build a fertilization stone as centrally as possible to all fertile blocks and assign both your workers to it.
4. Plant 4-5 log plants and 4-5 radishes.
5. Build large wooden chests (400 wood) as you can afford them until you have ~5000 storage capacity.
6. Dig out blocks on the same level around your starting area until you have an open area roughly 30x30 or so. While doing this, also build a research bench and train a scholar as soon as possible.
7. Research order I use is:
1. Top two tier 1 techs (better researchers and faster learning for dwarflings)
2. Cloth armor
3. All techs required to get to Better Plants (tier 3)
4. All techs required to get to cheaper objects (tier 4)
5. All techs required to get to faster research (tier 4)
6. All techs required to get to faster training (tier 4)
7. All remaining techs
8. Dig as straight down as possible, avoiding any unopened rooms (question marks) until you hit the grey stone levels.
9. Create a decent-sized room in the grey stone level (6x15 or so) and place three beds and a dining table.
10. You should have enough g
11. Cover all revealed areas with wood flooring and walls.
12. As soon as you've unlocked a tier 2 tech, train 2 more scholars and build advanced research benches (only need 1 extra if you've maxed the Research influence branch).
13. As soon as you've unlocked a tier 3 tech, replace your log plants with log trees and radishes with carrots.
14. As soon as you've unlocked Better Plants, plant 3-4 cherry trees and train 1 more worker (2 if you had to build two stones to fertilize everything).
15. Continue expanding in the grey stone area (avoiding question marks) until you have 300-400 titanium and 500-600 dragonforce (double this for the final region). Sell dragonforce to buy marble and upgrade all your research benches. You can also upgrade your scholars to researchers if you have the extra resources.
16. Upgrade your spawn pool again (2500 gold upgrade) when possible and recruit dwarflings up to pop cap.
17. If you are in the last region (The Infested Mountain or The Tower of Magicus), or going for the king's objective in The Elven Settlement, upgrade your spawn pool to max (5000 gold) when possible and recruit dwarflings up to pop cap (not necessary for The Elven Settlement).
18. Once you have resources stockpiled and have researched the the faster training for warriors tech, turn all remaining dwarflings into warriors and build one of the highest-quality training dummies for each warrior you have.
19. Wall in your prince with a bed and dining table to be safe if you have the first Military influence tech.
20. Wait for your warriors to train until all dummies have been destroyed or no dwarf is training at any of them (sometimes they bug out and dwarves refuse to use them)
21. Upgrade your dwarves as much as possible, selling dragonforce to buy other resources where necessary. Get whatever upgrades you want.
22. Finally, open up every area you need to get the objectives. Objective rooms can usually be identified by their large size and/or being surrounded by undiggable blocks.
Following this, it takes me roughly 60-90 minutes per level