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Note for beginners: Although this is the third achievement to earn in the Icy Land, it is much more difficult than the first two. Lands grow more difficult the more treasures you collect in a land as the enemy spawn rate increases dramatically, so it is recommended that you do not collect more than 10 treasures in a single land until you are more experienced and ready to take on this greater challenge.

To earn this achievement, you will need to have a greater understanding of the Icy Land. First of all, the most fundamental mechanic here is heat: Your body creates heat as you walk around, and this is represented by the surrounding tiles changing colour - from blue first to white, then red, then yellow. The tiles will gradually return to the surrounding temperature once you have left the area. The first thing this affects it the Ice Walls - you can heat these up just like the floor, and once they grow hot enough (above 0°C) they will melt, allowing you (and monsters) passage.

The next thing to understand is the monsters - you may have already noticed they do not quite act in the same way.
The simpler enemy is the Yeti - this enemy uses line of sight to find the shortest path to you and moves in that direction. If there is no path to you visible on-screen, the Yeti will not move.
The Icewolf, however, tracks you using heat. This enemy is blind, and cannot see the walls - instead, it simply tries to move directly towards the hottest tile on-screen (this is typically, but not always, the tile you are standing on). This allows you to trick it, but can also make its movements more erratic. It is also worth noting that as 'heat' does not exist in most other lands, the Icewolf cannot enter them and will instead wait at the border between lands.

Finally, you have some extra support to help you defeat these enemies as they appear in ever-greater numbers.
The Bonfire appears as a brown spark on the map, and starts inactive. If you move next to one, you can click to activate it - this does not cost you your turn, so you can do this while on the run from enemies. Once the bonfire is active, it will generate a large amount of heat in the area, melting any nearby walls and confusing the Icewolf into losing track of you.
The Orb of Flash appears as a white circle with a serrated ring around it (like a sawblade). Once you collect it, it appears in your inventory for 77 turns, waiting to be activated. Then, the next time you make an illegal move (trying to walk into a wall or next to an enemy) or attack an enemy, it will be consumed. This destroys all enemies in a two-tile radius of you, and also fills the area with a large amount of heat (similar to the Bonfire, but this heat will eventually dissipate). This orb is quite valuable if you find yourself surrounded.
Finally, the Orb of Winter appears as a blue circle with a simple ring. Collecting one grants you its power for 30 turns, during which time your body temperature drops even lower than the surrounding area. Ice Walls will form in a trail behind where you walk, and the Ice Wolf will run away from you rather than towards you. It does not last a long time, but it should keep you out of trouble. You can also use the walls created to block off the Yeti, but be careful not to wall yourself in because you cannot melt the walls until the Orb's power fades.

Once you have a decent understanding of the Icy Land and its inhabitants, you should be able to collect 25 Ice Diamonds in a single game and earn this achievement.

Note: If you are playing in Orb Strategy mode, you will instead need to collect 50 Ice Diamonds to earn this achievement. You will need to have a good understanding of when to use your orbs in order to reach this lofty total. This will be covered in the guides for achievements that are exclusive to Orb Strategy.