Vengeance Mode is a mode that can be attained as an alternative to Expert Mode in the world creation menu. It is unlocked by defeating the Moon Lord in Expert Mode, and then killing all three mechanical bosses at the same time within thirty minutes. Doing this will proceed with a message saying 'Somewhere, somehow, new choices can be made!' in the chat.
This mode makes changes to every boss, as well as granting some new weapons and armor that you can use to make some extremely powerful items. All bosses are also ever-so-slightly more aggressive.
King Slime: HP increased to 4,500, and will only teleport on top of the player. Drops Jewel Launcher.
Eye of Cthulhu: HP increased to 6,500, can spawn servants in Phase 2, and can shoot tears. Drops Teardrop Staff.
Eater of Worlds: Now 250 segments. Drops Murasama.
Brain of Cthulhu: 3,500 HP. Summons creepers in phase 2. Drops Blood Butcherer.
Skeletron: Spawns with four arms. Drops Skallium Ore.
Wall of Flesh: 16,400 HP. Eyes are immune.
All Mechanical Bosses: 80% more HP, Damage, and Defense.
Plantera, Golem, and Duke Fishron: Twice as much HP, and can charge/charge more.
Lunatic Cultist: 67,000 HP.
Moon Lord: Six hands.