Mafia Jumps is one of the Mafia Town challenges provided by Death Wish in A Hat in Time. It plays out identically to She Came from Outerspace, where Hat Kid must chase Goofy Mafia until he gives up the Time Piece he found. However, an added challenge is present: limited jumps, where Hat Kid can only perform so many jumps before completing the act, otherwise she dies when jumping for the 16th time.
As stated, the level performs near identically aside from the limitation to the quantity of jumps, requiring the player to be frugal with how they jump and how many times.
Consider that the chase portion itself is very demanding in how one jumps through the air, with several portions typically requiring two or three jumps just to reach the next platform. Any jump that can be saved leading up to the chase is valuable, especially for the bonus objectives of further reducing the total jump count.
Simple jump-saving tricks should be looked into and attempted, like performing a single jump and covering the distance between two platforms with a dive and dive cancel, as well as getting up to the edge of the massive hanging 'Mafia' sign and doing a double jump and dive cancel to catch onto the platform past the wooden structure with the wall climbing, saving a jump though being quite a bit riskier as a result.
Using the Sprint Hat
Some jumps in the act are mandatory. Jumping while sprinting using the Sprint Hat will give the player the height and distance of a double-jump while only advancing the jump counter by 1.
Using the Ice Hat
With the Ice Hat, the player can perform a minor hop if the use button for hat abilities is slightly tapped, allowing Hat Kid to do some minor platforming sections such as climbing the concrete pipes at the start of the chase.
Furthermore, it can be employed to skip the entire gambit of Mafia Town by finding a nearby Ice Hat panel and bounding up to the center of town, diving towards the large platform that the Goofy Mafia starts from.
Note that while the Ice Hat removes the mud from Hat Kid, a scared Goofy Mafia will always run in fear as lightning flashes and covers Hat Kid in a silhouette, meaning the only portion where Hat Kid needs to be coated in mud is at the very beginning of the chase.
When finishing the act and collecting the Time Piece, one can jump up to the Time Piece and end the run there, or they can use the Ice Hat to jump onto one of the boxes to the left side, and dive off of them to the Time Piece without costing that jump.