The first Batteryman monster is Batteryman AAA:
When this card is Normal Summoned or flipped face-up, you can Special Summon 1 "Batteryman AAA" from your hand or Graveyard.
Batteryman AAA has an optional Trigger Effect. If you activate it while Normal Summoning it, it can be negated by Pulling the Rug. Since you can choose to Special Summon a monster from the Hand, it does not target another copy of itself. Note that it refers to "Batteryman AAA" only, so you cannot Special Summon Batteryman AA with this effect.
The other Batteryman monster is Batteryman Fuel Cell:
If you control 2 or more face-up "Batteryman" monsters, you can Special Summon this card from your hand. Once per turn, you can Tribute 1 other "Batteryman" monster to return 1 card your opponent controls to the owner's hand.
Fuel Cell has an Inherent Special Summon to Summon itself from the Hand. Its second line is an Ignition Effect, which tributes a Batteryman monster as a cost, and it targets one of your opponent's Cards. You can tribute Fuel Cell itself. As usual, if you target a S/T Card that doesn't remain on the Field, and it is chained, it will not return to the Hand.
And finally, the Spell Card support for the theme is Electromagnetic Shield:
Level 3 or lower face-up Defense Position Thunder-Type monsters you control cannot be destroyed by battle. Destroy this card if you control a face-up Attack Position monster.
Shield has two very simple effects. The first one is your usual battle protection effect. The other one is an effect that doesn't use the chain, which will destroy Shield immediately if you control a face-up Attack Position monster. It should be evident that Damage Calculation is applied normally (for example, with monsters that have a trample effect).
Moving into the next theme, we have the spaceship Delta Tri:
If this card destroys an opponent's monster by battle, select and activate 1 of the these effects: ● Select 1 appropriate Union monster in your Graveyard and equip it to this card. ● Select 1 face-up LIGHT Machine-type monster you control, and return it to the Deck. Then draw 1 card.
Delta Tri has two mandatory Trigger Effects, which you activate at the End of the Damage Step, and both target. The first effect is treated as equipping an Union monster by its own effect, so all of their rules apply. Not that we have reviewed them yet, though Q_Q The second effect doesn't return the monster as a cost, and drawing a Card is not simultaneous with this return. Since Delta Tri doesn't care where the destroyed monster ends up after being destroyed in battle, this effect will activate even if Delta Tri is not face-up at the End of the Damage Step. Of course, this creates some disadvantages, as you are unable to equip Delta Tri, and you have one less candidate to return to the Deck.
Supporting Delta Tri, we have Trigon:
Once per turn, during your Main Phase, you can equip this card to a Machine-Type monster you control, OR unequip it to Special Summon this card in face-up Attack Position. While equipped to a monster by this effect, if the equipped monster destroys an opponent's monster by battle, select and Special Summon 1 Level 4 or lower LIGHT Machine-Type monster from your Graveyard. (A monster can only be equipped with 1 Union Monster at a time. If the equipped monster would be destroyed, destroy this card instead.)
This Union monster is not too different from others. Its only peculiarity is its effect to Special Summon a monster. This effect is a mandatory Trigger-like effect that activates at the End of the Damage Step, and it targets the Machine monster. Note that since this is the effect of an Equip Spell Card, it must remain face-up in order to activate and resolve, so it won't activate if the equipped monster is destroyed in battle (or if you save it with Trigon).
The support Spell Card for this mini-theme is Dragon Laser:
Send 1 "Trigon" equipped to a face-up "Delta Tri" you control to the Graveyard, and destroy all monsters your opponent controls.
This Quick-Play Spell Card is pretty powerful, as it packs the effect of the never-forgotten Raigeki. It targets 1 "Trigon", and since it targets, it means that it is not a cost. You need to succeed in sending Trigon to the Graveyard in order to destroy the monsters.
That covers another small chunk of Cards from TSHD, but there's still almost half a set to go! If you have any questions, feel free to drop me an e-mail at ness00[at]gmail[dot]com.