What are the conditions to get the "Who Needs Tygan?" achievement?

The info text for the Steam achievement "Who Needs Tygan?" reads "Beat the final mission using only conventional gear".

What exactly does conventional gear mean in that context?

Solution 1:

Apparently, coming from someone who did check in the game's files for the achievement conditions :

Of note is that this only applies to the final mission, you can happily upgrade throughout the game, just make sure your squad going into the final mission is downgraded. (Tip: Psionics/Dominate is AWESOME).

Only Tier 0 items:

• Assault Rifle, Pistol, Shotgun, Cannon, Sniper Rifle, Sword, Gremlin Mark I, Psi Amp, Grenade Launcher
• Nanofiber Vest
• Medikit
• Frag Grenade
• Flashbang
• Smoke Grenade
• PCS Upgrades
• Weapon Mods

Exceptionally, the following upgrades are allowed: (since you can't downgrade)

• Alien/Plasma Grenade (Permanent upgrade to Frag Grenade)
• Nano Medikit (Permanent upgrade to Medikit)
• Smoke Bomb (Permanent upgrade to Smoke Grenade)

Forbidden Items include (not comprehensive - ANYTHING not in the list above may be bad):

• Skulljack
• Battle Scanner, Mindshield, Mimic Beacon
• ANY Special Ammo (Talon, Venom, Dragon, AP, etc.)
• ANY Special Armor (EXO Suit, Warden armor etc.)
• ANY Special Grenade (Gas, EMP, Acid Grenade/Bomb, etc.)
• ANY better weapon (Advanced Grenade Launcher, Arc Blade, etc.)

In essence, the game checks the inventories of all soldiers and makes sure that you only have Tier 0 items, with the exception of the three permanent upgrades (Alien Grenade, NanoMedikit, Smoke Bomb) and any drops you got throughout the mission.

Interestingly, the Nanofiber Vest is allowed as well.

Source : XCOM Reddit