The missiles created by the mythic magic missile spell "bypass the shield spell and similar effects that block the non-mythic version of this spell," but the brooch of shielding, despite the name and despite using the spell shield in its construction, does not, technically, block the missiles from a magic missile effect: "[I]t can absorb magic missiles of the sort generated by the spell or spell-like ability[, absorbing] up to 101 points of damage from magic missiles before [the brooch] melts and becomes useless."1
The brooch of shielding (1,500 gp; 0 lbs.) is, however, extremely narrow in function, can't be recharged, and occupies the wearer's neck slot, which is extremely valuable personal real estate. By using the rules for Adding New Abilities to magic items, with the GM's permission, a brooch of shielding effect could perhaps be added to another inexpensive and slotless item (e.g. an ioun stone (dull gray) (25 gp; 0 lbs.)) for 2,250 gp. (Both brooch and stone are wondrous items and, as there's no trend of magic items that absorb spells occupying the neck slot, adding the brooch's effect to the stone shouldn't be an issue; see Altering Existing Magic Items under Magic Item Slots for Pathfinder's heartless limits to such effects.)
But, because using the brooch to defend against mythic magic missiles is reliant on a technicality, the GM could rule (and, perhaps, equally technically, maybe correctly, seeing as how the shield spell is used in the brooch's creation, after all) that the brooch is no defense against the mythic magic missile, ruling that the terms block and absorb are here close enough to be synonyms. This GM, though, given the lengths the creature's gone to to make itself—briefly!—immune to something as rare and weird (in this GM's campaigns, anyway) as magic missile effects, would let such a defense function, even against a mythic magic missile spell. The brooch will be slag soon enough under an assault by any competent mythic magic missile Metamagic Master mage.2
An empowered (+2) maximized (+3) quickened (+4) 1st-level magic missile spell cast by a creature possessing the trait Metamagic Master (magic missile) (−1) spends one of that creature's 9th-level spell slots. While a level 20 caster's version of such a magic missile spell can be cast as a swift action, it deals only 25+((5d4+5)/2) points of damage, or, on average, about 43 points of damage. That's not only embarrassing but also pitiful for a 9th-level spell slot. A similarly beefed up mythic magic missile deals a more impressive 90+((20d4+10)/2) points of damage, or, on average, about 120 points of damage—more impressive but still a 9th-level spell slot and costing of 2 uses of mythic power. Although, the line-of-sight range and ability to bypass spell resistance and even spell immunity are excellent benefits of mythic magic missile. I can imagine the efficacy of such a spell being taught in wizarding classes: reliably picking off foes on the horizon is pretty cool, and for a caster with the correct trait, the spell's only 5th-level if it needn't be quickened (the mythic power cost will limit its usefulness, though).
So while your party's warrior can worry about this spell, the party's unlikely to encounter the spell a lot unless the GM routinely punishes players by dealing their PCs (45+((10d4+10)/2)) points of damage seemingly out of nowhere by sticking flying, greater invisibility-using mythic tier 4+ wizard 9s on every horizon.
1 I must add here that I really enjoy authors making absolutely certain the reader knows what a particular rhetorical flourish actually means in game terms, like melts and becomes useless so that there's no argument about a melted brooch continuing to suck up magic missiles. My favorite example of this is from AD&D's Monster Manual (1978): "If a [mind flayer's] tentacle hits it will reach the opponent's brain in 1-4 melee rounds and draw it forth, immediately killing the creature" (70), y'know, just in case a player at the table argues, "Hey, I'm a fighter! What do I need a brain for!?"
2 Probably far fewer creatures should have the trait Metamagic Master than do. The regional trait originally appeared in the Dragon Empires Primer as Wayang Spellhunter (14), and, as the name and provenance suggests, a GM may limit the trait's availability to those from a region like Golarion's Minata which is populated largely (but not exclusively) by wayangs.