This card can be destroyed in many ways allowing you to Special Summon "Yubel - Terror Incarnate". Some of these ways are:
Using the effect of the same card that Summoned it, like "Limit Reverse" or "Doom Shaman". Summon this card using "Limit Reverse" during your opponent's End Phase, then switch it into Defense Position during your Main Phase, or Summon this card with the effect of "Doom Shaman", then Tribute "Doom Shaman" in the End Phase to pay this card's cost. Since "Doom Shaman" left the field, this card is destroyed, activating its effect.
In case of Spell or Trap Cards that destroy the Summoned monster(s) after the card itself is removed from the field (like "Call of the Haunted" or "Safe Zone"), they may be chained to an opponent's card which will remove them from the field, or the player can forcefully remove them with cards like "Double Cyclone" and "Malevolent Catastrophe"
Using the effect of "Chain Destruction" to destroy the other copies of the Summoned "Yubel" in your Deck.
Using your own card effects to destroy this card, such as "Shield Crush".
"Fire King Island" allows you to destroy this card from the hand, eliminating the need to Summon it. Additionally, when another Field Spell Card is activated or Set and "Fire King Island" is sent to the Graveyard, it will destroy "Yubel - Terror Incarnate" to make for an extremely fast way of summoning "Yubel - The Ultimate Nightmare".
"Hardened Armed Dragon" can be an advantage and disadvantage to this card. If you Tribute Summon "Yubel" using "Hardened Armed Dragon", you don't have to Tribute monsters to make "Yubel" survive, but because it can't be destroyed by card effects anymore, it can't evolve into "Yubel - Terror Incarnate" unless the effect of "Yubel" is negated.
If your opponent tries to subvert this by refusing to summon any new monsters, you can respond by bringing monsters that are easily summoned to his side of the field, such as "Grinder Golem" or "Nightmare Archfiends".
After you Special Summoned this card with "Mystic Tomato", "Damage Condensor" or "Damage Gate" in your opponent's turn, simply activate "After the Struggle" in your turn to destroy Yubel and an opponent's monster by attacking him, and then Special Summon "Yubel - Terror Incarnate" with Yubel's effect.
If you have another monster in your field, you can use cards like:
Combo this with "Nightmare Archfiends" or to do at least 6000 points of damage to your opponent if he attacks your "Yubel".
Summoning "Grinder Golem" to the opponent's side of the field leaves behind two "Grinder Tokens"; if your opponent is forced to attack "Yubel" and cannot destroy the tokens, they can be tributed to "Yubel" to keep it on the field.
Try to summon both "Grinder Golem" and "Nightmare Archfiends" to the opposing field at the same time; one token can be tributed to activate the Archfiends, and the other can be consumed by "Yubel" to keep it on the field, leaving it as the only target. With forced attacks, this can result in a One Turn Kill. (Do note, however, that this can be risky as it hinges entirely on your opponent lacking a way to immediately deal with "Yubel" - if it is destroyed/negated before the opponent's Battle Phase, you could find yourself on the receiving end of the OTK.)
Note that "Savage Colosseum" will increase your opponent's life points by 300 for each attack.
"The Calculator" will have at least 3600 ATK while "Yubel" is on the field.
Use "Swing of Memories" while "Doom Shaman" is in the Graveyard and "Yubel" is either at the hand or Graveyard. "Swing of Memories" will let you Special Summon "Doom Shaman" who will be able to summon "Yubel" from the grave. When the turn ends "Doom Shaman" will be destroyed and so will "Yubel" allowing you to summon "Yubel - Terror Incarnate" onto the field.
This card can be used with March of the Monarchs to prevent it destroying itself (since March prevents destruction via card effects, including a card's OWN effect), however this will also prevent summoning Yubel - Terror Incarnate. Still, this can be a good thing - Terror Incarnate destroys your opponents' monsters, but you may wish to keep their monsters on the field so they can keep attacking Yubel and damaging your opponent.