Subverted: Alex is pretending that small attacks hurt him too much.
At high levels, the various compensations he receives for having such low health, such as death protection and an incredibly high dodge rate make him almost impossible to decisively harm. Whether this makes him a Game Breaker or not depends on the rest of the game.
Double Subverted: ...However the next small attack does.
Parodied: Alex is an overweight, out of shape, anemic mess that can't take a punch to save his life. So he spends every day immolating anything vaguely threatening in his immediate vicinity, from ornery cows to evil armies.
Alex is an anemic, hemophiliac invalid who can be killed with the slightest touch, but he is armed with various attack spells ranging from lethal to apocalyptic, and he lives in the strongest fortress ever built, having healing spells and force fields under his sleeves just in case.
Deconstructed: Alex develops a sense of insecurity over being super powerful and extremely fragile and his fear of being attacked first leads him to kill people he could easily have dealt with diplomatically, or even people who startle him.
In a world of long-range firearms that allow someone to attack him from far away with no defense, in the face of sneaky backstabbing enemies, and other tricks, Alex is simply useless in the battlefield.
Reconstructed: Which he realizes is an overcompensation, so he develops defenses that help him dodge attacks so he doesn't get hurt.
...And then the heroes develop anti-material rifles, block-busting laser cannons, and Earth-shattering bombs for him. Stealth is moot when Alex has auto turrets that could shred a mammoth in a second at the slightest detection.
Alex himself is already the master of the arts of acrobatics, stealth, hiding, and powerful long-range attacks.
Zig Zagged: Alex is a spindly atom bomb, except he's really tough, but that was just an illusion, only it turns out he's not that powerful, only to turn out to be a I Am Not Left-Handed.
Averted: Characters who are better on attack than defense aren't absurdly so.
Enforced: "Alex's incredible attacks are a defining trait of his, but she needs a weakness for the sake of Competitive Balance.
Lampshaded: "Everyone, guard Alex! He really, really needs it."
Invoked: Alex believes that the best defense is a good offense, so he purposely skips all the defense lessons and concentrates on her attacks.
Defied: Alex trains up his physical strength and becomes a Magic Knight, Kung-Fu Wizard or the something equivalent to that.
Discussed: "So did you skip all the "How to take a punch" classes in wizard school? Oh right, you flunked out"
Conversed: "He's like a walking Papier-mâché atom bomb."
Back to Glass Cannon...but get into melee range as fast as possible, or you're toast!