Very similar to the "Impregnable Defense" trophy/achievement, this one requires you to collect a total of five tier 8 weapons. For reasons that may not be immediately apparent, this is actually somewhat more difficult than collecting five tier 8 pieces of armor.
For one thing, there aren’t usually too many different tier 8 weapons per weapon type, and of the tier 8 weapons available for the weapon, there likely won’t be five of them you actually need to make. Unless you switch between weapons you’ll find yourself effectively burning materials and Zenny, which may be distasteful, especially since there’s plentiful pieces of useful tier 8 armor. Heck, defeating Nergigante alone will unlock the ability to craft ten pieces of tier 8 armor (defeating each Elder Dragon unlocks a five piece armor set, which comes in two versions), while many tier 8 weapons require you to farm Xeno’Jiiva. Finally, don’t forget that each weapon requires you to advance up a weapon tree, creating many - if not all - of the lower level variants along the way. Not only does this cost quite a bit of Zenny (around 100,000 Zenny per weapon, in some cases), but a wide variety of materials, both Low Rank and High Rank monster materials and various bones and ores, etc.
That being the case, you’ll probably need to complete the main questline, then farm Xeno’Jiiva as the optional quest to do so becomes available until you have the parts to make the five tier 8 weapons you need. After which, you’ll need to climb the weapon tree, fighting other monsters and gathering materials as necessary to progress through the lower tiers. Once the fifth tier 8 weapon is crafted, this trophy/achievement should pop.