The first sentence of this card’s text means that after you complete an attack with “Tyrant Dragon”, if there is still a monster on the opponent’s side of the field, “Tyrant Dragon” can immediately attack again. You cannot attack with another monster in between, and then attack a second time with “Tyrant Dragon.” If there are no monsters on your opponent’s side of the field after “Tyrant Dragon”’s first attack, “Tyrant Dragon” does not gain a second attack.
“Tyrant Dragon” cannot attack more than twice, even if there is another monster remaining on your opponent’s side of the field after the second attack.
“Tyrant Dragon”’s first attack does not have to be the first attack of the Battle Phase. You may attack with another monster, then with “Tyrant Dragon”, then again with “Tyrant Dragon” – if the opponent still controls a monster.
Suppose you control “Tyrant Dragon” and another monster (“Dark Magician” for example), and the opponent only has 1 monster. You attack with “Tyrant Dragon” and destroy their 1 monster. Then you declare a direct attack with “Dark Magician” and the opponent activates “Scapegoat” to Special Summon 4 “Sheep Tokens”. A replay occurs, and that means “Tyrant Dragon” was the last monster to attack, so it may attack again, and attack one of the Sheep Tokens. Then you can attack with “Dark Magician”.
The opponent may activate Trap Cards that target “Tyrant Dragon”, but their effects will be negated and the cards destroyed.
When you Summon “Tyrant Dragon”, the opponent can activate “Torrential Tribute” or “Bottomless Trap Hole” and destroy “Tyrant Dragon” because neither of these Trap Cards target. (However, “Trap Hole” does target and its effect will disappear if activated.)
When you attack with “Tyrant Dragon” the opponent can activate “Mirror Force” and all your Attack Position monsters, including “Tyrant Dragon”, will be destroyed. This is because “Mirror Force” does not target.
You may activate “Last Turn” and select your “Tyrant Dragon” as the monster to keep, because “Last Turn” does not target.
When you Summon “Tyrant Dragon” the opponent can activate “Solemn Judgment” or “Horn of Heaven” to negate the Summon.
You can activate “Call of the Haunted” to Special Summon “Tyrant Dragon”. After it resolves, “Call of the Haunted” will be destroyed and “Tyrant Dragon” will remain on the field. You must still Tribute a Dragon-Type monster to perform this Special Summon, in accordance with the text of “Tyrant Dragon”.
If you activate “Monster Reborn” to Special Summon your opponent’s “Tyrant Dragon” in your opponent’s Graveyard, you must still Tribute a Dragon-Type monster from your side of the field. If you do not control a Dragon-Type monster, you cannot select “Tyrant Dragon” as a target for “Monster Reborn”.
You Tribute a Dragon-Type monster when the effect that Special Summons “Tyrant Dragon” resolves, not when it activates. So if you activate “Monster Reborn” and target “Tyrant Dragon” and your opponent chains “Imperial Order” and negates “Monster Reborn” you do not Tribute a Dragon-Type monster. Likewise, if you control 1 Dragon-Type monster on the field, and activate “Monster Reborn”, and your opponent chains “Ring of Destruction” to destroy your only Dragon-Type monster, you are unable to Tribute a Dragon-Type monster when “Monster Reborn” resolves and its effect disappears.
You may Tribute a face-down Dragon-Type monster when you Special Summon “Tyrant Dragon”.
Even if “Tyrant Dragon” was destroyed by “Dark Balter the Terrible” or some other monster that negated the effect of “Tyrant Dragon”, you must still Tribute a Dragon-Type monster if you Special Summon it because this is a condition, not an effect.