The Exterminator achievement in Terraria is worth 25 GamerScore and is awarded for defeating every boss. Most bosses are made available by summoning them with crafted items and/ or through certain times of the day.
This is a complete list of all bosses required for the achievement, including their locations and whether or not they are hard mode.
King Slime|A rare spawn in the Forest during day time. Will not spawn near your player spawn point. King Slime can also be summoned with a Slime Crown, which can be crafted from a Gold/ Platinum Crown, 99 Gel on a Demon Altar. King Slime has no time limit or window.|No
Eye of Cthulhu|Chance of spawning at night once the player has at least 200 health, 10 defense and 3 or more NPCs. These requirements will only allow Eye of Cthulhu to spawn once. Subsequent spawns must be facilitated through use of a Suspicious Looking Eye during the night. You can craft a Suspicious Looking Eye using 6 lenses at a Demon Altar. Eye of Cthulhu must be killed before sunrise.|No
Skeletron|Skeletron is summoned by speaking to the Old Man at the Dungeon entrance. It must be night time, otherwise the Old Man will ask you to come back. Skeletron will despawn if you die, and can only be defeated once per world.|No
Wall of Flesh|The Wall of Flesh is the hardest non-hard mode boss. It is summoned by throwing a Guide Voodoo Doll into lava while in the Underworld. Note that you must have the Guide housed, as this will sacrifice him. All players will be forced to engage the Wall of Flesh. If you don’t defeat the Wall before it traverses the entirety of your world, you will be killed. Defeating the Wall of Flesh will automatically place your world into hard mode. This state is irreversible.|No
The Destroyer|Summoned anywhere during the night by using a Mechanical Worm. This item can be crafted from 7 Souls of Night, 6 Rotten Chunks, 5 Copper Bars and 5 Iron Bars. You will need a Mythril Anvil. Note that you must defeat The Destroyer before sunrise, otherwise it will despawn.|Yes!
The Twins|Summoned anywhere in the world by using a Mechanical Eye, crafted from 7 Souls of Light, 3 Lenses, 5 Copper Bars and 5 Iron Bars. The Twins can only be summoned during the night, and must be defeated before sunrise to avoid them despawning.|Yes!
Skeletron Prime|This boss is the hard mode version of Skeletron. It can be summoned by using a Mechanical Skull. This item is crafted from 5 Souls of Light, 5 Souls of Night, 30 Bones, 5 Copper Bars and 5 Iron Bars. Aim to defeat Skeletron Prime before sunrise, else he will enter “God Mode”, giving him extra defense and killing you instantly if you stand still.|Yes!
Ocram|Note that this boss is console only. Ocram is summoned by using a Suspicious Looking Skull. This item can be crafted from 10 Souls of Light, 10 Souls of Night, 1 Mechanical Skull, 2 Mechanical Eyes and 20 Adamantite Bars. Ocram must be summoned during the night.|Yes!
Here are some helpful videos that may help defeat the bosses listed above, and obtain the achievement.
Thanks to TheStandardGamer for this video!
Thanks to CrimsonGamingChannel for this video!