My tip for the megaminx is that all the algorithms are the same as the 3x3x3, they just go off at weird angles. If you can keep your focus on a corner and treat it like a 3x3x3 you should be good. The last layer is odd to get the edges, I use the same algorithms, but the patterns to look for are different and the edges move a little differently since there's an extra edge that moves around. The corners are pretty easy in the middle portions, so I just put them in place while being careful about the completed parts.
I have that same Megaminx, it's a good one! I'm also not going for records etc. I don't even time myself doing the mega -- it's more for stress relief when I don't feel like trying to break my 3x3 records.
I basically used a pdf of instructions to do the megaminx beginner's method, until I had it memorized. It's basically all F2L until you get to the top layer, then there's a couple of simple algs (sune, etc.) to memorize to do the top.
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4x4x4 is the next logical step, but megaminx is actually easier: no new algorithm is needed (if you come from the "beginner method"). Figuring out all layers (except the last one) is pretty easy. Then I suggest you do some 3x3x3 algs to see what is affected. Anyway, that’s what I use too, no world record in sight either!
4x4x4 parity is the real hassle. I use commutators to remember it, and it’s pretty inefficient too :p
People keep saying that but I'm still struggling to map the f2l move to the 12 sides of this thing. It seems important the order in which I solve each pair. Plus just having the 12 colors to deal with, and I'm red green color blind. I need to spend more time with it still.
What I do is : insert corners first, then edges. Corners are easy. For edges, I do an insert "beginner"-style (URU'R' U' F'UF). (Since it can breaks the adjacent side, I pair the edge with the corner on a higher layer, that is doing 1 turn on the face). Just experiment with it, I’m sure it will "click" at some point ;)