Upgrading weapons is actually quite easy and if you upgrade a weapon of level 49 to 50 you would get the other weapon upgrade achievements as well.
Only requisite is that you need other weapons in your inventory so you can upgrade, you can obtain these by buying them at a town or doing the pillar killers game in the shop.
How to upgrade:
1. Press Y on the controller
2. Go to Custom
3. Choose Synthesize
4. Choose weapon to upgrade
5. Choose the weapons you want to use as material to upgrade
6. Upgrade! On the top you can see the level (usually a + x) which will get added onto the more weapons / higher quality weapons you use as material.
Upgrade a weapon to level 50 and the achievement should pop.
Hope this helps!