Are the [All-natural sugar cane] and [Last chance to see] achievements just luck-based or is there a specific way to get them? to get the [All-natural sugars cane] achievement you need to harvest a golden sugar lump and to get the [Last chance to see] achievement you need to burst the near-extinct shiny wrinkler. is there any specific way to do those things or is it just luck.
It is just luck. The golden wrinkler for [Last chance to see] appears 0.01% times and [All-natural sugar cane] has a chance of 0.06-0.11% of a golden sugar lump.
Although you have to trigger the Grandmapocalypse for wrinklers to spawn. If you want to know how to trigger it go here:
The odds of getting each type are exceedingly low, which is why those are shadow achievements that don't give milk or count towards "completion percentage." There are minor ways that you can improve your odds however.
[Last Chance to See] - there is no way to improve the odds of spawning a shiny wrinker which appears at a 0.01% chance or 1 in 10,000. The best way of obtaining one is by popping wrinklers as soon as they spawn in order to roll those dice as many times as possible. If you have all research upgrades purchased and are in the final stage of the grandmapocalypse with no elder pledge (Angered), wrinklers will spawn the fastest. There are also ascension upgrades to increase the speed at which wrinklers spawn at any level of the grandmapocalypse. Unholy Bait causes wrinklers to appear 5 times as fast, and Elder Spice increases your maximum wrinklers to 12 so you can get 20% more RNG calls per game tick.
[All Natural Sugar Cane] - The base chance to get a golden sugar lump is 0.075% or about 1 in 1333. This however can be improved with the aura Dragon's Curve which almost doubles the chances to 0.1466% or about 1 in 682. This is still extremely low, and you'll only get one chance per day at the base growth rate. However, there are several ways of decreasing the time that it takes for sugar lumps to mature, including the temple worship Rigidel and some ascension upgrades. The shortest possible time sugar lumps can take to fall and collect automatically is around 20 hours which means you can get an extra lump every 5 days or so. You can shorten this time by an extra few hours per day by collecting the lump when it's ripe or even when it's mature but unripe (if you don't care about losing the lump 50% of the time).