Spell and Trap Cards can be Set before using "Dragged Down into the Grave", and then use it to see your opponent's hand and your opponent must discard your "Dark World" monsters in your hand, then their effects can be activated.
This card and all "Dark World" monsters can be played with "Skill Drain", because a lot of the "Dark World" monsters have no effects that activate or resolve on the field.
Use "Fabled Raven" to help activate this card's destruction ability and put it in a position to be Special Summoned from the Graveyard.
Another option is to tune "Raven" with this card to Summon "Fabled Leviathan". When "Leviathan" is destroyed, its effect can be used to return "Raven" to the hand, revive "Grapha" with its first effect, and then re-Summon "Raven" to bring out another "Leviathan".
If "Beiige, Vanguard of Dark World" is Special Summoned with its effect, "Beliige" can be returned to your hand to Special Summon this card from the Graveyard, and then Normal Summon "Beiige", all with very little cost.
This card has destructive synergy with "Deck Devastation Virus" and "Eradicator Epidemic Virus" due to its 2700 ATK. Plus, the ability to bounce a "Dark World" monster to your hand to bring it back that same turn can cause a big headache for your opponent.
"Destruct Potion" or "Mystic Wok" can be used to a similar effect. Tribute "Grapha" to gain 2700 Life Points, then easily get it back on the field for an almost costless LP boost.
With the above strategy, "Leviair the Sea Dragon" can be Xyz Summoned. Then, use its effect to bring out any Level 4 or lower "Dark World" monster banished due to "The Gates of Dark World", and simply bounce it to Special Summon this card from grave. With this strategy, hand advantage is gained and get your boss monster to field at the same time.
When Spell/Trap Cards such as "Gateway to Dark World" or "Call of the Haunted" are activated, any of your "Dark World" monsters currently in your Graveyard can simply be revived, then return it to your hand to Special Summon "Grapha". This allows yourself to have a "Dark World" monster in your hand to use for its effect, or to revive "Grapha" when necessary.
Use "Junk Synchron" plus any Level 2 "Dark World" monster to return it to your hand and bring back "Grapha" easily. If "Drill Warrior" can be Summoned, "Junk Synchron" can be kept Summoning with the effect of "Drill Warrior" (and by extent, "Grapha") while keeping this strategy safe thanks to "Drill Warrior". "Drill Warrior" is also another discard method for the "Dark World" monsters, so they can be discarded and activate their effects, while "Junk Synchron" also lowers the discarding part of a bit as long as there is a proper target in your grave.
This card can be send directly from your Deck to the Graveyard with cards like "Foolish Burial" or "Fiendish Rhino Warrior", then Normal Summon any "Dark World" monster and this card will be grabbed in your first turn.
If this card in your Graveyard would be banished, use "The Forces of Darkness" to put it into your hand along with one other monster that would be banished - preferably another copy of this card (if there are any).
"Imperial Iron Wall" can prevent "Grapha" and your other "Dark World" monsters from being banished in the first place.