Challenge Running is the act of placing restrictions on yourself as you play through Paper Mario to increase the difficulty of the game. In contrast to speedrunning, where some restrictions can be placed, players are encouraged to take as much time to prepare to complete the challenge. Optional bosses such as The Master and Kent C. Koopa are generally required as part of a challenge run.
There are a variety of common challenges one can try.
List of Challenge Runs
As the name suggests you are required to complete the game without ever upgrading your HP stat, thus always having 10 HP as your maximum health. This challenge is often paired up with other challenges such as Mario Alone. Mario cannot reach level 20 during this challenge since this will force to upgrade HP.
Using Chet Rippo HP can be further decreased to 5 HP. This is called a Danger Mario Run. This isn't objectively harder than 10 HP on its own since the player can constantly take advantage of certain badges like Last Stand and Power Rush.
In a BP only run, only BP is allowed to be upgraded at level-ups, while HP and FP should remain at their base 10 and 5 respectively. The player should try not to exceed level 10 since otherwise they would have to upgrade HP or FP. Avoiding unrequired combat and using moves or items that defeat enemies without them dropping Star Points are key not to reach level 11. If a player reaches level 11, they could upgrade FP, and treat it as if they only have 5 FP (e.g. you have 10 FP, but you make sure it never decreases below 5FP) in such a case the run should be still seen as fair.
In this challenge run, Mario cannot use neither the jump or the hammer in battle. Lighter versions of this run that ban only the jump or only the hammer are also possible, called Hammerman and Jumpman respectively.
The goal of this challenge is defeating The Master's third form as early as possible. So far without any additional restrictions added, Koop has found a consistent strategy for a Level 4 Mario to defeat The Master before going to Mt. Rugged.
In this run Mario and his partner are only allowed to use act on even turns of a battle. During odd turns, Mario and his partners are required to choose the "do nothing" command and cannot guard enemy moves either.
Level Zero requires the player to complete the game with the following stats: 10 HP, 5 FP and 0 BP. Similarly to BP Only they will need to upgrade BP on every level-up while never equipping badges. The player also cannot upgrade any partners in Level Zero and its variations.
Level Zero also has three variations that change its difficulty further.
Level One: An easier variation of Level Zero which allows 3 BP to be used during the run.
Level Negative One: A harder variation of Level Zero that requires game completion with 5 HP, 5 FP and 0 BP. Health must be decreased to 5 HP as soon as possible, as such, the first level-up must go to FP and Chet Rippo must be visited immediately.
Like the name implies, during a Mario Alone run, only Mario is able to act in battle. The partners must always use the "do nothing" command.
A scavenge run forbids using items obtained in shops or Lil'Oinks in battle. In addition, visiting Tayce T. to cook is also prohibited. It's not much of a challenge on its own so it is best combined with other challenge runs. Not using any items in battle is equally possible in many challenge runs.
For this challenge the player must pick one partner. As soon as this partner is unlocked, he or she is the only partner that can be used in battle. Other partners can be out sometimes (i.g. you're forced to have Watt out for Fuzzipede) but she's forced to use the "do nothing" command at all time.
At the end of the day, if you are willing to try a challenge run, you're the one setting those restrictions on yourself. Don't feel burdened by the conventional restrictions, if you want to try out Level Zero, but with partner upgrades or Even Turn, but you're allowed to guard on Odd Turns, feel free to do so.