I'm not an expert of photogrammetry, but I'd like to know if there is a specific shooting method for large objects in order to use them into 3D apps. I'm not talking about textures, but capturing pure 3D mesh. As far as I know, I need to shoot the object moving around it at 360. Let's suppose I want to shoot a huge cliff, the problem is that I cannot go 360 but just in front of the cliff, so from one side to the other one. Since in this case I'm missing the 360 3D part, is it still valid?
As to the meat of your actual question:
"do you need a full 360° to successfully execute photogrammetry?"
The answer is "no, you don't".
What you do need is a range of angles around and above and below the face normals of your subject, and as @user287001 mentioned, it's best to do this in one drone session, in around a half hour, to keep your lighting roughly consistent.
You then need software, and though there are some free ones which work, they're not as good at interpolating where you have too little data. Reality Capture (Capturing Reality dot com) is ~ $100 for an indie license, and the AEC industry pros use Recap Pro from Autodesk for ~ $40/mo - both of these solutions will interpolate well from small to medium data sets, both accept up to 2500 images for one project's imagebase, and both will output pretty high quality meshes.
The real question you face is how much money you want to sink into this, and that goes to what your use-case is: are you intending this for a hobby 3D modeling effort, or are you thinking of "getting into photogrammetry" - in which case some investment in decent full-featured and robust photogrammetry processing software and a decent drone and capture imager seem like good thoughts.
There was a user on the Modo forums who for years kept plugging away at photogrammetry - at first it was pretty rough and ready, with arduous workflows and middling results, but starting about three years ago it began to get better and better - and then suddenly a year and a bit ago become amazing. He was using what was then called PhotoScanner - is now Agisoft's Metashape - whose hobbyist package is I think ~ $175 - and that one too has a lot of powerful tools and utilities. I remember he was using meshmixer (which is free) for mesh cleanups once he'd derived the mesh, and then bringing that into Modo for some pretty incredible results.
Hope this helps.
Make a test run. You can easily get free photogrammetry programs and trials of commercial programs. Do not expect anything usable from those areas which aren't seen well in at least 2 photos taken from substantially different directions.
You have also another problem. The daylight can change substantially during your walk to the other side of the mountain. Photogrammetry cannot deduce how the shadows have moved due the light changes.
If one cannot keep the light stable during the session or the target moves between the shots, the whole idea is hopeless. In photogrammetry studios they often have a bunch of identical cameras which shoot at the same moment.
If you cannot walk around the mountain, you get only that part of the 3D surface which exist in more than one photos and is seen from different directions. Others generally appear as holes. If you shoot only upwards, there surely are holes because your camera cannot see horizontal top surfaces.
Flat featureless areas will stay indefinite, no matter how many photos you have of them.