Monster Hunter Rise

Well-done steak can be cooked by using Raw Meat with the BBQ Spit.

Press LB + X to select whilst out and about, then active the BBQ by pressing X. When the music stops press B. If you're too slow you'll get burnt meat, if you're too fast you'll get rare steak

To ensure a well-done steak every time, Pay attention to the spit, About a second or so after the music stops the meat will change colour but only slightly noticeably, Press B after the colour has changed and before it changes again to burnt meat.
Update: I found it easier to notice the change when using a top down view of the spit-roast with the camera, GrimaceTheGrey has commented saying its half a rotation after the music stops.

Rinse and repeat 30x getting Well-done steak and the achievement should unlock.

The fastest way to do this would be simply to run into expeditions, cook the 10 raw meat you can carry, go to the tent to refill & repeat. Mine popped when returning from the expedition.

You can hold 10 Raw Meat & 10 Well Done Steaks at one time. When out in the various biomes, hit LB + X. If you have no other items gathered, and are at the entrance of the zone/done nothing else, the Spit will be 2 presses away. Select it and press X to place.

Instead of relying on music, I chose to count the number of spins that your hunter does with the grill crank. The spit handle starts at the up position. Let the handle turn 4 times. Right before it reaches the up position the fifth time (that's including the initial start), the meat will change color. Pull it off the spit by pressing B. That should get you a Well Done Steak rather than Rare or Burnt.

When you run out of Raw Meat and/or fill up with Well Done Steak, return to the tent and transfer items around to get another 10 Raw Meat and return the Well Done Steak to your Item Stash. Repeat until you have 30 Well Done Steaks.

You need to actually return to Kamura for this to pop. When you have your 30 steaks, and return to the village, you'll get an additional notification on the results screen listing Well Done Grillmeister. That's when the achievment pops.

You can hold 10 Raw Meat & 10 Well Done Steaks at one time. When out in the various biomes, hit LB + X. If you have no other items gathered, and are at the entrance of the zone/done nothing else, the Spit will be 2 presses away. Select it and press X to place.

Instead of relying on music, I chose to count the number of spins that your hunter does with the grill crank. The spit handle starts at the up position. Let the handle turn 4 times. Right before it reaches the up position the fifth time (that's including the initial start), the meat will change color. Pull it off the spit by pressing B. That should get you a Well Done Steak rather than Rare or Burnt.

When you run out of Raw Meat and/or fill up with Well Done Steak, return to the tent and transfer items around to get another 10 Raw Meat and return the Well Done Steak to your Item Stash. Repeat until you have 30 Well Done Steaks.

You need to actually return to Kamura for this to pop. When you have your 30 steaks, and return to the village, you'll get an additional notification on the results screen listing Well Done Grillmeister. That's when the achievment pops.

This achievement involves cooking Raw Meat into Well-Done Meat on the BBQ Spit 30 times while on a Hunt or Expedition Tour.

Gathering
Raw Meat can be obtained by killing and harvesting the "Small Monsters" found in the environment. You may also receive Raw Meat at the end of a "Large Monster" Hunt as part of the reward.

BBQ Spit
Ensure you have the Raw Meat in your Item Pouch before starting a Hunt or Expedition Tour (you can carry a maximum of 10 per run). Once you've spawned at camp hold and press to move your equipment wheel around until you land on the BBQ Spit. Release and press to place the BBQ on the ground. This will instantly start the cooking mini game and consume 1x Raw Meat.

Cooking Mini-Game
Over the space of 10 seconds the Raw Meat will change into Rare, Well-Done & Burnt Meat. The key here is to press when the Raw Meat reaches the Well-Done state. To perfect this you can use either the visual cue of the meat changing colour, or the audio cue of the music jingle finishing. I personally found the visual cue most effective, pressing when the meat became a dark brown colour with white bone appearing at the tip. This is when the red Raw Meat changes colour for the second time while cooking.

Note: The achievement only pops when you leave a Hunt or Expedition, not during the cooking process.

See my video guide for more detail: