I'm not sure how many this will reach, by the very nature of this website anyone posting on it is most definitely NOT a casual player, but here goes.
Hi, so I'm a casually serious player. I put in a lot of hours but I don't belong to an established raiding guild, the highest M+ I've pushed was 9 and that was on the week of writing this when doing 4 mythic dungeons rewards a cache of Heroic Antorus raid loot. I mostly log in to maintain high levels of order resources to keep my order hall gold-farm running, collect transmog gear and to do LFR.
I like to think that I show that casual =/= bad. I don't really sim things out but I take my performance pretty seriously. I know from some PuGs that I can keep up with heroic level geared raiders even in LFR gear by playing smart (and in all likelihood those raiders not being very good.)
At this point I've completed the Mage Tower challenge for:
Blood DK
Unholy DK
Fury Warrior
Prot Warrior
Ret Paladin
Prot Paladin
Havoc DH
Veng DH
BrM Monk
Enhance Shaman
That's the main spec of 6 of my 8 level 110 alts.
Last night while trying to help someone get their quest started to unlock the mage tower challenges (You'll want to do the broken shore unlock, then kill mobs until you get a random quest item and that'll unlock the mage tower challenge quests for any spec with over 35 traits in a weapon.) I came across a thread on the official forums talking about how Blizz was once again catering to elitists and no-lifers.
It was pretty clear a lot of the posters were dejected. It was a recent post as well.
So a lot of folks are maybe looking around and seeing the mage tower skins and feeling like they'll never have them, that they are out of reach and that they can't even come back later when overgeared next expansion to come pick them up.
Don't think that way. You can do it!
We have all sorts of guides and tips up - and I'd encourage anyone that has completed the challenges to share them as well here - but I thought I'd give folks some practical advice.
You're not going to 1-shot it. I don't know of anyone that's one-shot the challenge, I'm sure someone will comment below and I'm happy for them, but these challenges are not easy and even if you overgear them (which is pretty simple in just LFR gear) they can still beat you.
When you first go in you'll probably be nervous, even if you watched a guide or read on the fight you'll discover that the timing is all over the damn place on these things. Mobs have cast priorities based on timers, life left and even random rolls of what ability they'll do when. You'll find weird BS and randomness in ever encounter.
They are all meant to get you to play with all the abilities of your spec including your "oh shit" buttons. So don't get intimidated, look for a solution or talk in your guild or post here about what happened and while I'm sure you'll find a bunch of e-peens ready to tell you how terrible you are you'll also find helpful folks willing to go over things that are happening in the fight and how best to counter them.
Mostly though don't be afraid to practice and fail. Until you're comfortable with the fight you'll make all sorts of mistakes - some will be buffered by gear and not be that big a deal, others are damn stupid instant death that make you want to throw your keyboard through your monitor.
Last night I got the Enhancement Shaman quest done. It took roughly 50-minutes of wiping to get it down, many times running into a problem of overlapping mechanics that were complete bullshit, but I worked through them and you can too.
So please, don't be intimidated or discouraged. I know a lot of you have lives outside that require a lot of attention - we all do and one of the reasons the Mage Tower isn't up 100% of the time is so that we don't spend all day every day grinding on it.
Get into LFR, pick up your tier, you'll be overgearing the challenges and you can do them.
But they won't be easy, you won't get them down right away. You're going to have to work for these appearances and earn them, but you can do it. We're all rooting for you.