WARNING: Do not enter Zugzwang's Tower as soon as you crafted the Zugzwang's Tower Key!
Before you enter Zugzwang's Tower, make sure your Tower Amplifier is fully charged in the Seasonal Garden(150% for Lords).
You should also need to have a good supply of Super|Brie+ (about 200 or more) to last you for one run in the Tower. If you don't have enough Super|Brie+, Gouda is a good alternative.
Other than that, you should also get a Pawn Pincher from the Seasonal Garden's Trapsmith.
Mystic/Technic Pawn Pincher (Tactical
Cost: 643,750 gold
Power: 60, Power Bonus: 5%, Attraction Bonus: 20%, Luck: 0, Cheese Effect: Stale (Technic)/Fresh (Mystic)
Both of them have the same price and their stats are almost identical. It is highly recommended you get both of them. If you're low on gold, just buy one and then buy the other one later.
If you're done preparing, we shall enter Zugzwang's Tower!
Zugzwang's Tower
The mice in Zugzwang's Tower are themed by chess pieces. There are two teams here, the Mystic and Technic teams.
Like chess sets, you'll have to catch the mice of a certain team in this order:-
8 Pawns -> 2 Knights -> 2 Bishops -> 2 Rooks -> Queen -> King
The mice from before can still be attracted though. For example, at Rook stage you'll still might attract pawns, knights and bishops.
Remember the Tower Amplifier in Seasonal Garden? In Zugzwang's Tower, the Tower Amplifier will increase your trap's power.
For Lords, the maximum amount of amplifier is 150%. This means that your trap power will increase by 150%, this doesn't increase luck though.
Better watch out! When the Amplifier starts to drop below 100%, your power and luck will start to decrease and at 0% you'll be kicked out of Zugzwang's Tower back into the Seasonal Garden.
The Amplifier will decrease with each mouse caught, depending on the type of mouse. Failure to attract will cause it to lose 3%, so it's good to have high attraction cheese like Super|Brie+ or Gouda. Missing a mouse won't affect the anplifier at all.
Unlike the Seasonal Garden, leaving the Tower will cause your amplifier to reset to 0%, so leaving the tower isn't recommended unless your amplifier is really, really low.
With that let's get started on the first stage, the pawns.
Pawn Stage
First of all, you should decide which team you want to catch, be it Mystic or Technic. if you've decided which team, use the correct pawn pincher to attract the pawns you want.
The pawn pinchers special effect is that it attracts more of the certain pawns, since at this stage the chances of attracting the correct pawn is about 50%. The pinchers also helps to capture the respective pawns much easier.
You can also try arming the Wooden Base with Target to reduce FTAs and to avoid accidentally catching pawns from the other team. You'll need to catch 8 pawns to attract the Knights.
Knights, Bishops, Rooks and the Queen
Knight Stage
The Knights are tougher than pawns, so from here on use your most powerful Tactical trap setup. Beware though, mice from the other team will sometimes get captured. Get 2 Mystic/Technic Knights and you'll be able to attract the Bishops.
Bishop Stage
Bishops are harder to catch than both pawns and knights. Once again use your strongest Tactical trap. By now, you'd probably caught some mice from the other team by accident, so be careful. Capture 2 of them and you'll attract the Rooks.
Rook Stage
Rooks are the second toughest mouse to catch in a team, so arming some charms is quite nice. Same thing, arm your strongest Tactical trap setup. If you've got 2 Rooks of the same team, you can now attract the Queen.
The Queen Stage
The Queen is the strongest mouse in the team, so once again arm your strongest Tactical setup. Arming some charms which increases your power/luck is also a nice touch. Once you finally get your Queen, you can attract the King.
The King
The King is one of the weakest mouse in a team, so you should have no trouble catching him. in fact, you can try arming the Wooden base with Target at this stage to reduce chances of FTAs and accidentally catching other mice.
Once you've caught your king, you'll automatically be transported back into the Seasonal Garden.
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Mystic Crystal/Droid Jetpack
The Mystic King will drop the Mystic Crystal while the Technic King will drop the Droid Jetpack, but both loot are uncommon drops. If you're lucky enough to get one, you can craft the following weapons.
Recipe:-
1x Mystic Crystal + 1x Blackstone Pass Trap Blueprints + 4x Coal
= 1 Blackstone Pass Trap
= 1 Obvious Ambush Trap
The Blackstone Pass and Obvious Ambush blueprints can be bought in the Seasonal Garden's General Store for 1,100,000 gold each. Droid Parts are sold in the Bazaar's General Store for 7,750 gold and the Coal is a loot from the Catacombs.
Obvious Ambush Trap/Blackstone Pass Trap (Tactical)Power: 3,000, Power Bonus: 15%, Attraction Bonus:-, Luck: 12, Cheese Effect: Very Fresh (BPT)/Very Stale (OAT)
3,000 power and 12 luck, these two weapons aren't much stronger than your First Move, so why craft them? For starters, they have a special effect in the Tower. Blackstone Pass is more effective in catching Mystic mice and doing terribly against Technic mice, the Obvious Ambush does the opposite.
Outside of Zugzwang's Tower, these two traps are of not much use, you can try to skip them and take your chances with other stronger Tactical traps. They're just here to make your tower runs easier and help you save your Amplifier.
The Chess Master
Another loot the two Kings drop are the Mystic Curd and the Technic Cheese Mould respectively. These two loots are the key ingredient to craft type of cheese known as Checkmate Cheese.
Recipe:-1x Mystic Curd + 1x Technic Cheese Mould + 12x Ionized Salt
= 3 pieces of Checkmate
1x Mystic Curd + 1x Technic Cheese Mould + 12x Ionized Salt + 6x Magic Essence
= 9 pieces of Checkmate
Checkmate cheese have a special effect in Zugzwang's Tower. When you catch a King in the tower, you will not be sent back to the Seasonal Garden. Instead, you'll stay in the tower and able to attract the mastermind behind the Seasonal Garden and Zugzwang's Tower, the Chess Master! It is recommended that you craft Checkmate as much as possible before getting it.
The Chess Master can be attracted after you've caught a King with Checkmate. During the Chess Master stage, arm your strongest Tactical setup with Checkmate. Like the Queen, this mouse is quite hard to catch. 
Once caught, he'll drop the Master Bindings which we'll need to craft a super-base! He'll also drop Zugzwang's Left Sock. Why would a mouse be holding a sock that belongs to Zugzwang? If you'd notice the Chess Master's left foot, it doesn't have a sock. Could he be the legendary wizard Zugzwang? We'll never know for sure, for now the sock is a collectible item and fetches a good price in the Marketplace.
Anyway, let's craft a mighty base! The downside is that you need 67,750,000 points to craft it.
Recipe:-
1x Master Bindings + 1x Spellbook base Blueprints + 3x Torn Mystic Page + 3x Torn Technic Page + 6x Tiny Platinum Bars
= 1 Spellbook Base
The Torn Mystic Page is dropped by the Mystic King. The Torn Technic dropped by the Technic King. So yeah, you'll have to do at least 6 runs before you can craft this base.
The blueprints are sold in the Seasonal Garden General Store for 936,000 gold and the Platinum Bars are sold in the Training Grounds General Store for 60,000 gold each.
Power: 500, Power Bonus: 14%, Attraction Bonus: 5%, Luck: 7, Cheese Effect: Fresh
Now that a mighty base! 500 power is amazing and 7 luck is great. In fact, it's one of the strongest bases in the whole game!
If you're lucky, you'll find that the Rook or Queen will drop something important, although Knights and Bishops also drop it. By now, you should have it. Yes, it's a map piece! It's called the Crystal Library Card! This means you can access the Crystal Library.