For convenience, here are descriptions of the custom elements in all the entries. This is ordered by placement, starting from 12th place and working up to first. This does not give the full details on all the elements, but should cover anything not explained by the entries themselves.
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×12th Place - That Familiar Feeling
Girkle - A portal that swaps objects between two locations. Somewhat hastily implemented.
11th Place - Fire! Fire! Fire!
Firetrap Counter - This is the name of the object in the editor. Player is disarmed, but can place a limited number of firetraps by pressing the special command key. The counter tells you how many you have left.
When the counter reaches zero, pressing the special command key activates all firetraps once. They will all deactivate if something dies in one.
10th Place - Two Headed Serpents
Two-Headed Serpent - This is something of a joke entry. The titular serpent isn't actually a serpent, and its special property is that it can be body-pushed. However, pushing it will only prevent it from attacking on that turn and will not stun it on the next. The lack of an explicit explanation seems to be part of the joke.
9th Place - Horticulturalist's Headache
Briar Seeds - Player is disarmed, but can place a briar root with a force arrow under it with the special command key. The force arrow matches the direction the player is facing at time of placement.
There are some secret rooms with unique mechanics relating to this: seed bags, which give you one root each (the main level lets you place as many as you want) and tokens which swap between standard weapons and briar seeds.
8th Place - Darting Around
Uni-Dart - A single dart. Can be picked up by standing on it and pressing the special command key, then you can fire it by pressing special command again. Each one faces a specific direction and will always fire in that direction.
Uni-Dart Splitter - Fire a Uni-Dart into this, and it will be destroyed and Uni-Darts will be placed on all open surrounding squares. The orientation of these darts is based on their position relative to where the splitter was - for instance, a dart that lands north of the splitter's location will always face north.
7th Place (tie) - When Mass-Production Breaks
Conveyor Belts - These start out inactive. A special tile ("Conv-Belt Activate") turns them on and off when something moves onto it. When active, conveyor belts move objects on them in the direction they're pointing.
Monsters on conveyor belts will not change the way they're facing. If an object that creates a stepping stone in shallow water is moved into deep water by a conveyor belt, it makes a stepping stone. Don't ask me how that works.
7th Place (tie) - Smite-Blasting 101
Rocket Launcher - A custom weapon. You are disarmed, but your orientation is maintained through scripting trickery (although this has some weird side effects and at least one room plays with the weird side effects). Pressing special command fires a rocket, which moves forward one tile per turn and explodes when it hits an obstacle.
The rocket is a solid object and can be pushed.
6th Place - Swampy Basement
Leech - Can only move over water (including shallow water). When the player or another valid target gets within two tiles of it, becomes an Angry Leech which can move over land as well.
Note that this only applies if the player is close enough when the leech's turn happens. If the leech is three tiles away and moves to be two tiles away, it does not become angered on that turn. Also, the leech will not move on the turn it becomes angry.
5th Place - Duplication Lab
Doppelganger - Duplicates monsters that are next to it for one turn. If a monster moves next to it but is killed or pushed away on the next turn, it does not duplicate. Fatal if player moves next to it.
There are some special rules for situations where the Doppelganger will instantly duplicate, explained in scrolls in the first room.
4th Place (tie) - Koopa Bros' Fortress
Bombette - Monster that explodes if it is blocked from moving (only after it starts moving). There are several special rules for this element, which are explained in scrolls on the level.
4th Place (tie) - Net Benefits
Net Token (N Token in editor) - Disarms player and gives them a net. The net allows one monster at a time to be captured by pressing special command when next to it. The captured monster can be released by pressing special command again.
Note that as implemented in this level, you cannot get the sword back after taking the net, so make sure you're done with it before stepping on the token!
3rd Place - Beethro Plays Hockey
Puck - When pushed, moves in a direction until it hits something. Has effect of stabbing whatever it hits.
If pushed through hot tiles or fire traps, it will continue moving until it hits a wall (or falls in a pit/water), destroying all monsters in its path.
Forms a stepping stone in shallow water.
2nd Place - Pulse Cannon Testing Track
Pulse Cannon - When something (either Beethro or a monster) is in its line of sight, it fires a turn later, destroying everything in its path. Always faces a specific direction.
Pushable by all weapons.
1st Place - Pixie Desert
Pixie - Flying entity that tracks Beethro. Pressing special command will cause Beethro to switch places with the pixie. Not harmful, not a required target, and immune to weapons.