Here is a sneak peek of some of the pyro achievements you can get in TF2 to unlock your weapons and how you can do them.
You can now also get the weapons through radom drops as you play the game but with the achievements, you're guaranteed to get them if you really want a specific weapon.
Map: Achievement_Pyro_Final - You can Google for this map or look it up on known sites that provide TF2 maps or achievement maps and then just download it into your TF2 folder to play it for these achievements.
Since this map is made specifically for the Pyro, it's a lot easier to get a lot of the achievements just by using this map.
If you don't use this map, you can still get the achievements listed below with a friend.
The Pyro achievements are probably the easiest to get.
All 22 achievements can be acquired here.
Start off by having your friend go Spy since a lot of the achievements can be found this way.
Freezer Burn: Provide enemies with freezecam shots of each of your taunts.
This is very easy to get with the next few achievements listed.
After you kill your friend with your fire axe for Lumberjack taunt him with your flamethrower equipped and your fire axe equipped.
Taunting with your shotgun out will give you OMGWTFBBQ.
Dance Dance Immolation: Kill 3 enemies while they're taunting.
While you are killing your friend with the fire axes have him taunt before you kill him.
Doing this three times will give you this achievement and Lumberjack if you kill them with the fire axe.
OMGWTFBBQ: Kill an enemy with a taunt.
You will get this while you're doing Freezer Burn.
Lumberjack: Kill 3 people with your axe in one life.
Have your friend spawn and sit there for you.
Pull out your fire axe and take them out three times in a row.
Clearcutter: Kill 6 people with your axe in one life.
Just like before have your friend spawn and kill him an additional three times and you'll have a total of six fire axe kills.
These are very easy to get in a row.
Camp Fire: Kill 3 enemies in a row, all within the same area.
This achievement should come up after you get Lumberjack.
If not you should get it while doing Hot on Your Heels.
Once you have completed enough achievements to hit milestones, you will be able to unlock weapons for the pyro.
Then you can choose which pyro weapon you want to play with from your menu.