Weather radar may be your best and only friend but you will get there. If you can see it avoid the anvil (tail as you say?) and fly on the upwind side. If you have to go on the downwind side deviate one mile for every thousand feet in height that the TS is. If the TS is 40 000' deviate 40 miles. At least.
Here's a copy and paste form a pprune post that deserves reading again.
Aircraft most certainly are NOT designed to withstand entry into cumulonimbus storms. I agree with the remainder of your statement.
Right now my sole function is flying turbojet airplanes into storms for weather research. I generally fly a Lear 35A into convective weather to study it, sample it, and in some cases, experiment with modifying it.
DO NOT FLY INTO THE STORM!!!
Think of the thunderstorm as the Finger of God. You're a gnat. There are forces inside more powerful than what you think they will be. Scott Crossfield, a well known name in flight test and aviation history, was killed not long ago when he flew through a thunderstorm; his aircraft broke up and he lost his life. The storm is not a respecter of persons; you may fly through one a dozen times or a hundred times and one the next one, it will take you. Don't put yourself, your aircraft, or your passengers or company in that position.
Weather radar is only partially able to see what's out there. Frozen precipitation doesn't paint well at all; dry hail, dry snow, ice, all can be invisible to radar. We hail, slush, graupel, and other features containing at least some liquid water are visible, but can be very misleading. What you think is a level 1 return or even a blank spot on the radar, can hide some very nasty surprises. Hail may not show up at all, and it can be very large, very fast, and do an increadible amount of damage, even far from a cell. Miles away.
Up and downdrafts have been recorded in excess of 12,000 fpm in the cells. Going into a sheer zone between such changes means a 24,000 fpm vertical shear, and your aircraft was most definitely not designed for that.
Ice buildup can be very rapid, and not at all where you expect it. Supercooled water between -10 and plus several degrees can form extremely rapidly; I've picked up three inches of ice in very short periods when penetrating cells, and others I fly with have experienced severe engine damage as a result of rapid ice buildup and shedding into intakes, etc. Even with everything working. Even when the last few penetrations through the same cell were uneventful. Even when it doesn't look so bad on radar. Even when a team of scientists are guiding the flight by radio, watching you on some very sophisticated radar...even with a team of scientists on board and a full suite of electronic sensors giving you detailed analysis of the storm and atmospherics as you go through.
When YOU penetrate a Cb, you don't have any of that going for you. What you have going for you is guesswork and luck, and that's no way to live.
Autopilot function may become impossible in convective weather. You're back to handflying it. If you're getting slammed, you may not be able to clearly see your instruments. You may be subject to injury. Your headset quite possibly won't even stay on your head. If you're below maneuvering speed, as you should be, you may find yourself stalling repeatedly. We often get the stick shaker and even the pusher when it gets rough, and we stay out of most of the serious weather.
As SP noted, weather can come from below with rapidity. When I start working a cell, I often make a pass through the upper parts of it first, and start making passes through the rising turrets alongside the main tower. Fresh starts are of the greatest interest, but these are often rising at thousands of feet per minute. Even if the convective activity at the surface isn't that great, the vertical velocity of rising air is cumulative. If a parcel of air rising at 300 fpm bumps into another parcel of air moving at 200 fpm, it now rises at 500 fpm, and soon bumps into more air rising at 400 fpm...now it's 900 fpm and rising. You get the idea. As this happens relative humidity in the parcel of air climbs, temperatures drop, and the parcel can remain liquid for a considerable time and well above normal freezing altitudes. On the same storm that 12,000 fpm vertical was located, the temp with liquid water was found at -38 C. High, wet, rough.
On another flight, what appeared to be a normal entry into a rapidly rising white puffy cumulus cloud turned out to be hail and weather that engulfed the ariplane, causing over three hundred fifty thousand dollars in damage to engine inlets, nacelles, damaged or destroyed fan blades, destroyed leading edges, radome, etc. In seconds. That with the penetration initiated with radar tilted down considerably to view the cell; it rose and enveloped the airplane quickly and with a vengence. You don't want to be there at a time like that.
When passing from one level of convective activity to another, inside the weather, the changes may appear subtle, but the results encountered (and the aircraft reactions) may be markedly diverse. A level 1 green return with speckles of yellow, suggesting level 2, appears benign sometimes. Almost calm. Elements of graupel and rapid ice buildup give way to dryness, and nothing, and then suddenly heavy rain. Doesn't appear like much on radar, but it's there, and on the second pass after a quick turn to re-enter the cell from the opposite direction, the character has grown ugly. Ice builds so rapidly it can't be shed. Noise, lightening, thunder we can hear, and then lightening strikes. Is this the time you want to lose your radar because of an electrical discharge or lightening strike? How about your isntruments, radios, or instrument displays?
We get frequent precipitation static such that one we're in the weather, we're not talking to anyone; we can't. The radios just hiss and growl, and at night we can see it corresponding to sporadic buildups of corona and St. Elmo's fire. Occasionally a discharge occurs; completely blinding if you happen to be looking out at a tip tank for ice or to see the St. Elmo's at the time. A few weeks ago it burned holes through our elevator, and melted pits down one tip tank, blew out static wicks, and put burns on the radome. In times past I've seen it burn holes through elevators, flaps, propellers, and melt pitot tubes, ice detectors, and AoA vanes in varying degrees. You don't want that.
Take great pains to avoid weather. What is inside, you shoudn't experience. There are things inside which can hurt you, disorient you, sap your performance, break your airplane, tumble your gyros, leave you covered in ice, and pull you to pieces. Not every storm is like that, but do you really want to pick and choose?