I'm standing at the top of a rocky outcrop with views out onto the floodwater plain which converges with the Hoanib river, towards the very northwestern tip of Namibia. The plain contains pockets of rainfall – rare in this part of the world – which is why it attracts so many of the desert-adapted animals who live here. And today, it has drawn a herd of elephants – around 15, including mothers, kids and a couple of dads – but also a massive, five-tonne alpha male, whose tusks are almost twice as tall as I am. “Interestingly,” says Geert, my softly-spoken guide from Wilderness Safaris (which runs several camps throughout the country), “this bull is currently on heat.” We peer at him for a few minutes, as he mills around with the herd, but then he decides to strike off on his own – stomping along the path that circles our outcrop, which suddenly doesn't seem high enough.

“Ah, he is frustrated!” relays Geert. Oh, goody. Apparently the lady elephants are not in season at the same time the bull is, so now he's in a foul mood, possibly sensing the smell of several humans in the air, and spoiling for a fight. Geert, however, has a cunning plan: to dart down the rocks to move the hefty safari vehicle out of the elephant's path, which would mean we could hotfoot into it safely. The elephant has other ideas; he's taking his time, stopping to siphon up dried mud from the parched riverbed floor and cover himself in it to help cool down from the 40°C heat (not something I'll be trying). In the end, we're stuck up there for a tense 45 minutes, waiting until the bull's decided to go back and see if he can sweet-talk one of the females into tugging on his trunk, or whatever passes for foreplay in the realm of the pachyderm.

Our undignified scramble down to the 4x4 before he changes his mind is henceforth known as 'Escape from Elephant Mountain'. If this sounds like the title of a Wilbur Smith novel, then it couldn't be more apt; spend just a week in this beautiful, bereft country and you'll be plunged into a land of dashing, daredevil bush pilots; encounters with animals who could kill you with one lazy swipe of a paw, or swift charge with a tusk; instinctive, seen-it-all guides, who can read the landscape like a large-print novel; sunsets so scarlet it's like the sky is illuminated with blood; and a jagged coastline pebble-dashed with the rusting steel skeletons of shipwrecks.

We face a five-tonne alpha male elephant whose tusks are almost twice as tall as I am

Namibia is the fifth-largest country in Africa (it covers nearly 825,000 sq km), but also one of the most sparsely-populated, with just two million inhabitants. It's composed largely of desert: the Namib (considered to be the oldest desert in the world) runs down the Atlantic coastline, while the Kalahari sprawls across the middle, overlapping into neighbouring Botswana and South Africa, and beyond. Colonised in the past by Germany and Great Britain, this year sees Namibia's 25th anniversary of independence from South Africa, to which it had been mandated in 1919 by the League of Nations.

Kulala Desert Lodge

At Kulala Desert Lodge, you can sleep beneath the stars on your very own 'star bed'

Its extraordinary landscape is unbelievably diverse – from the striking red sand dunes of Sossusvlei in the south of the country, to the arid brush of Damaraland in the north, it sets the scene for a series of incredible adventures. I started out at Sossusvlei, based in the nearby Kulala Desert Lodge, which has a distinctly Mexican, adobe-hutted feel and boasts a much-needed swimming pool for guests returning from an early-morning game drive.

This is not really lion or rhino territory; you will, though, spot giraffes, ostriches, and curve-horned oryx, who turn their heads to stare at every safari vehicle that drives by, before getting on with the serious business of chomping at whatever grass they can find in the scorched earth. Early morning starters are rewarded with a hearty lunch before going back out again in the evening, where each drive ends with a sundowner, watching the great ball of fire sink into the sand.

Thrill-seekers are in their element here: one game drive substitutes quad bikes for a safari truck, so we race over dusty tracks, leaving confused springboks and baffled oryx in our wake. You also have the option of a sunrise balloon ride, a great way of seeing the topography of the sinuous, curved dunes from high up. But even better is to see them at close range; and not only that, but to climb them.

Big Daddy is not a man to be messed with. In fact, he's not a man at all, but Sossusvlei's highest sand dune, standing proud at 325 metres of terracotta-coloured, tightly-packed, miniscule granules of rock. My guide, Joas, quickly sizes me up and decrees that I shall be taking the 'short cut' to the top, rather than starting at the tail end of the dune. He's right to; despite starting at seven in the morning, when the air is cool and fresh, it's tough, hard going, and I'm sweating profusely by the time I reach the first crest.

According to Joas, some people can run up the dune in 25 minutes. I look at him doubtfully. “Don't worry, that's only for really fit people!” he laughs. Every step you take, you sink back twice as far, as the sand shifts underneath your feet. It's sometimes demoralizing, and there are many, many times when I come to a sudden halt and Joas has to wait patiently for my ragged breathing to get back to normal.

My other worry is, how are we going to get back down? I look suspiciously down the steep sides of the dune, but Joas assures me that reaching the bottom, where the white, cracked salt and clay pan of Deadvlei lies, will be a breeze. In the end it takes me an hour and 45 minutes to get to the top, and then about five minutes to reach the bottom. This is achieved by galloping downwards, while leaning back so you don't topple over; it's an utterly exhilarating experience. Deadvlei is a dramatic reward; fringed at one end by black, withered, petrified trees, which contrast dramatically with the white ground, red dunes and blue sky. It's like a child's vivid drawing.

Big Daddy is not a man to be messed with. In fact, he's not a man at all - he's a sand dune

Moving on to the next camp, in Damaraland, I have the chance to track the endangered black desert rhino. Desert Rhino Camp works with trackers and conservationists to try and preserve these magnificent animals from poachers, to whom they are still seen as highly prized because of their tusks (the Chinese in particular still use them to make aphrodisiacs). There are now only around 25 within the local area, and they aren't tagged, so trackers have to use traditional methods of tracking their hoof-prints and spoor to find and observe them.

Despite being very short-sighted, rhinos have acute senses of smell and hearing, so any attempt to get within 100 metres of them has to be done downwind. The trackers are experts and within an hour of my first drive, they've found one – a large male nicknamed Getaway, weighing just over a tonne, who seems to be quite happily minding his own business in the shade of a tree. To get closer we have to slowly inch our way in a circuitous fashion until we're loosely opposite him. Despite the trackers insisting that he's feeding, so is calm and relaxed, it's proper heart-in-mouth stuff: if he got wind of us, he would charge. And with a top speed of 45mph, I wouldn't fancy my chances against him and his lethal-looking tusk. After gazing at him in awe for about 20 minutes, the trackers lead us back to the (relative) safety of our vehicle. “We had a rhino attack a car once – he tore through it like his tusk was a can opener!” one laughs.

Death is never far from your mind out in the desert, whether it's spotting the benevolent-looking milk bush – a tangle of green tubes filled with a lethal, milky substance which can kill a human in minutes; or the ripped-up remains of various animals – we pass several skulls, and a haunch bone with some of the giraffe's distinctively-patterned fur still attached – and nowhere is that more apparent than on the Skeleton Coast.

A 20-minute flight from my final quarters, Hoanib – a stylish, Scandanavian-looking safari camp – the coast, over the past century or so, has been incredibly unforgiving to anyone who found themselves unlucky enough to wash up on its bleakly beautiful beaches. With no food or water for hundreds of miles, sailors had a choice: die with their wreck, or in the middle of a sandy nothingness. Lions roam freely here (this camp also works with conservationists to assess their breeding patterns), so however it happened, it would have been a pretty nasty way to go.

The fact that you're currently reading this means that I came back from Namibia physically unscathed – despite the various horny elephants and rampant rhinos I bumped into. I returned with incredible memories of a landscape that will be etched on my consciousness forever.

Getting there

Black Tomato can arrange a luxury seven-night safari holiday to Namibia staying at Kulula Desert Lodge, Desert Rhino Camp, and Hoanib Skeleton Coast Camp from £5,989pp. Price includes return flights with South African Airways from London Heathrow via Johannesburg, accommodation on a full-board basis, light air craft transfers, and excursions. For more information or to book, call 020 7426 9888; blacktomato.com