dtgreene: Try doing as much damage in one hit as possible. Is it possible to one hit kill a boss? (It doesn't matter if the method isn't actually possible.)
With certain setups and specific bosses, it's possible to deal enough damage to kill them in one or two attacks. However this is due to those bosses consisting of multiple parts and requires those parts to be lined up correctly while using an attack that pierces all of them.
Try taking as much damage as possible. (I saw a video where the player fell down a hellevator and took over 15,000 damage)
Is it possible to heal large amounts? (I am thinking 1k+ HP, far more than you could actually attain.)
Highest amount of damage would probably be falling from the very top of the world to the very bottom and then being Stoned by a Medusa with enough duration for you to land. Being Stoned increases fall damage and prevents any of the Immunity to Fall Damage accessories from working. I'm 99% certain that the Portal Gun doesn't carry over any fall height.
Without cheating it is currently impossible to heal more than 599 HP from a single effect. This requires a full compliment of Heartstones (granting 400 HP), Life Fruit (+100 HP) and an active Lifeforce Potion (+20% HP), being at 1 HP while talking to the Nurse for healing. You'd need a decent timing to achieve this since you regenerate health outside combat (and you have to survive with just 1 HP left).
Try making a Hollowed base. Try doing this in a pre-hardmode world. (Is there any risk of corruption when Hardmode is triggered?)
Once you trigger hardmode, a v shape with one line being corruption and the other hallow will be released from the bottom center of the world.
See if you can build a base in space.
Try fighting bosses in space.
3 bosses will be hard/impossible to fight in space due to their mechanics. Another 2 will enrage (extra speed, damage and armor) and murder you asap due to taking them out of their biome. Bases are quite possible in the space biome, just look out for Wyverns in hardmode.