Red Right Hand

COMBAT TRAINING
Hellboy can use any weapon he can put in his hands to some degree of proficiency. He has a natural handle on most sharp and point or blunt and thwacky weaponry; maces, battle axes, spears, swords, the words; he prefers Western or European weaponry to anything else, however. He is also extensively trained in hand to hand combat, using a mish mash get the thing dead fast style. Between his natural strength and speed, atop his training, he is a lethal weapon in hand to hand combat; were not even including the sheer unstoppability of the Right Hand Of Doom (see powers.)
Hellboy’s gun training and modern weaponry, however, is not so extensive; unlike his skill with hand to hand weaponry, which seems nearly inborn, gun work took training, and he simply prefers weapons with fewer moving parts. This is not to say he's not decent with his gun, it's that he finds that they tend to be less reliable then, oh, a claymore sword. He's just funny that way.

WEAPONCRAFT AND INNOVATION
Hellboy can, given equipment and materials, design his own weaponry and rounds for them. He primarily uses this to create special rounds -- from the Creature Killers to other sorts of special rounds (radioactive, stunners, explosive shells, armor piercing...) He can, also, make knives and basic small weaponry from common objects in a desperate situations. Never know when you're gonna need to take a statue and club something to death with it.

EXPLOSIVE ORDINANCE
Hellboy is experienced with both modern and archaic ordinance. He can set you up the bomb, and take that vampire's castle sky high! He can, with the right equipment and household chemicals, make you a bomb if he really wants.

PARANORMAL
If it exists in lore, Hellboy likely knows it. Unicorns, faeries, ancient demons; he does his research and does it well. Hes made a career of sixty years out of monster slaying, and hes one of the best. He is a repository of random knowledge about the occult and the creatures that lurk in the shadows of it. It's just the matter of remembering just which hell beast or werewolf he's dealing with -- there are so many, after all. A little reading always helps jog his memory, but likely he knows the basic weaknesses of most common critters, and with some time to prepare, can handle more rare and unique things.
With the right training and preparation, Hellboy can conduct rituals from works of magic and books, if he has the right things on hand. He cannot do it without preparation, equipment, and study, though -- he's NOT a mage, and he cannot cast spells on the fly. He's just a very talented occultist.

FBI TRAINING
Investigation is not his forte, but Hellboy does know the basics. He also knows basic stealth and assassination techniques (though they are not his preferred methods) and other basic things, from combat parachuting, piloting a jet pack, to emergency first aid to how to tie up bad people real tight. Its a catch all skill for things that only a pseudo-government agent or other trained operative would likely know. After all, he's basically James Bond, paranormal style.

LINGUIST
If it's a dead, ancient, unspeakable, demonic, or otherwise weird language, likely Hellboy can read you sonnets in it, translate the bible or Shakespeare into it, or otherwise converse fluently (alas, he is not geek enough to do Klingon love poetry. Sorry.). That doesn't mean he doesn't know plenty of living languages, either; if it's spoken by natives in Europe, Hellboy can speak it, and same goes for the Middle East (cradle of civilization, after all) and most Asian languages. His African dialects are sketchy, and he doesn't know many Native American dialects. Still, he can fumble his way through most languages he needs too.

SURVIVAL
Doing a lot of investigation into the paranormal takes you into strange, distant places, and living in them is often difficult. Hellboy has been trained to survive almost anywhere; his supernatural constitution really helps out here, but still, finding food and water is a necessity to the big guy. However, you could drop him the Urals or the Sahara, and he'd probably still manage to make it back to civilization -- or whatever passed for it -- alive.

WELL EDUCATED
This is a catch-all skill to cover that Professor Broom covered... well, a lot of things. He was given an Ivy League education in the sciences; he is a passable medic, chemist, and he knows his physics. He's also well read, enjoys philosophy, and likes classical literature (though not as much as Abe does) and writes clearly and coherently. One can never say that Hellboy doesn't know his stuff. He does. Very much so.

SIXTY YEARS EXPERIENCE
This trait is to note that Hellboys been around a long time, and knows quite a bit of basic living, from driving to body building. Hes packed in a lot of living and a lot of trivia, from movies to music. This is a catch all skill to represent life experience, from boating to wood crafting, general house repair and basic mechanical know-how. He's not AMAZING at any of these skills, but he knows enough to get by in a pinch -- just don't expect him to be an expert in any general, 'normal' field; he just knows enough to get by.

BASS SINGER
Hellboy sang bass in the Roswell Base choir; he doesn't advertise the fact that he can croon, really -- it's not exactly a skill he needs in his line of work. But he can sing, and sing well. It's just that not a lot of things are meant for bass voices, really.