Unlike typical slime that flows and drip from a height, there is a new species of slime that is capable of scaling height in search of food. I am wondering how does a gloopy and slow moving slime without backbone or any kind of cartilage to support its own weight could scale tall places? My slime is biologically immortal but can still die and be digested when eaten by other animals.
"... they [cells] are highly structured in much the same way as our own bodies. They have a network of filaments known as the cytoskeleton (literally, “cell skeleton”), which not only supports the plasma membrane and gives the cell an overall shape, but also aids in the correct positioning of organelles, provides tracks for the transport of vesicles, and (in many cell types) allows the cell to move.
Here is a time-lapse video showing exactly what you want.
...slime molds ... form a structure called a pseudoplasmodium that moves over logs, bark, and soil at a rate of one inch per day. When food is particularly abundant, the slime mold changes. Some of the slugs form a base, while others become spores and stalks.
Here is another video. It shows that slime moulds can creep vertically upwards. https://youtu.be/Nx3Uu1hfl6Q
Lie down, open your mouth and stick your tongue out. Your tongue does not have bones, so how did you manage that?
You manage because your tongue is a hydrostatic organ, so it behaves just the same as a hydrostatic skeleton:
A hydrostatic skeleton, or hydroskeleton, is a flexible skeleton supported by fluid pressure. Hydrostatic skeletons are common among simple invertebrate organisms. (...) As a skeletal structure, it possesses the ability to affect shape and movement, and involves two mechanical units: the muscle layers and the body wall. The muscular layers are longitudinal and circular, and part of the fluid-filled coelom within. Contractions of the circular muscles lengthen the organism’s body, while contractions of the longitudinal muscles shorten the organism’s body. Fluid within the organism is evenly concentrated so the forces of the muscle are spread throughout the whole organism and shape changes can persist.
Organisms containing a hydrostatic skeleton have advantages and disadvantages. Their fluid shape allows them to move around easily while swimming and burrowing. They can fit through oddly shaped passages and hide themselves more effectively from predators. They are able to create a force when squeezing through rocks and create a “prying open” gesture. There is a lightweight, flexible component to them that allows this movement with very little muscle mass.
These organisms are also able to heal faster than organisms that contain hard skeletons. Healing in these organisms varies from creature to creature. However, if the cavity needs to be refilled, the "fluid" can easily be refilled if it is water or blood. If the fluid is some other type of liquid, it can take longer, but it is still faster than healing a bone. The common earthworm is also able to regrow damaged parts of its body.
These organisms have some relatively simple pathways for circulation and respiration. Also, these organisms have a cushion to allow protection for internal organs from shock. However, it does not protect internal organs from external damage very effectively.
Because the hydrostatic skeletons have limited ability for attachment of limbs, the organisms are relatively simple and do not have many abilities to grab or latch onto things. Organisms with complete hydrostatic skeletons need to be in an environment that allows them to re-fill themselves with their fluid that is necessary for survival. This is why hydrostatic skeletons are common in marine life. They have a large amount of access to the necessary elements for survival. Terrestrial organisms that have hydrostatic skeletons generally have a lack of strength because they are not in a fluid environment. If one were to expand its body too much, it would collapse under its own weight.
Hydrostatic skeletons are very common in invertebrates. A common example is the earthworm. Also, hydrostatic nature is common in marine life such as jelly fish, starfish, and sea anemones.
This ability to keep a shape may also explain how a relative of the slimes, the gelatinous cube, can keep its shape ;)
Snails do not have backbone or any kind of cartilage to support their own weight, yet they can climb and move and can reach up to 30 cm.
Cephalopods like octopuses and squids can grow even bigger, though they have the support of water.
Your slime can use the same internal mechanism, as they also need to move in some way.