Remove the woody ends of the asparagus and cut it into short lengths. Set aside the tips.
Heat the olive oil in a large frypan. Add the garlic and asparagus and cook 5 minutes. Add the mushrooms and stir. Pour in the white wine and let it evaporate, another 5 minutes. Add the asparagus tips for the last 2 minutes cooking time.
Meanwhile, cook the tagliatelle in salted water until al dente. Drain and add to the asparagus in the frypan along with a few tablespoons of the pasta cooking water. Season with salt and pepper and toss everything together well.