Battlemages are designed to be functional melee killers. People will tell you that heavily decked melee's are your bane. I would argue that a heavily decked warrior with the right weapon choice is anyone's bane…so pay that no mind.
The trick to playing a successful battlemage and playing one that is just so-so relies on a few things. Keep in mind that battlemages are like many other casters that do not have a reliable lag skill, so you need to be able to chase efficiently.
I play my battlemages with a melee mindset, not because they are LIKE a melee class as Foxx will tell you, but because they are a very offensive class. You need to always be putting the pressure on your opponent with spells and with chasing.
Dispel is your biggest friend vs melee. Most melee's are going to be equipped with pure hit/dam so a dispel is really gonna rock their world if you are dancing the right weapon and are fighting a race susceptible to sharpmetal. If they are magic resistant races, sharpmetal/meteor can really push some nice damage.
Sear is your "mega" spell. But knowing when to use it is key. My battlemages will almost always try to initiate a fight around 8am. That gives me a couple hours to soften up my opponent without showing my trump card. Even if it is a close battle and they have you on the run…let them chase you, and let them stay close. Once 11am rolls around, a nice dispel/sear or even just a blinding sear will turn the table.
Obviously Ogres make great targets with a magical dancing blade, their magic vuln(read dispel magnet) and Sear will pull unspeaks on them. I have three-hit killed Ogres before with just Sear alone.
Mana upkeep is the one thing all battlemage advice givers will have in common on their list. Some will tell you that cancellation is the way to go, some will tell you that having slow up 100% of the time is the way to do it. Don't feel as though you need to listen to any of them.
Battlemage is a very versatile class and being such allows you to play them in a variety of different ways. How do I deal with the mana upkeep? I either use a client that supports a tick timer or recently as I have been playing on a Mac client without one, I've just learned to keep a count going in my head while fighting. Sleeping at the right time will allow you to counter the mana drain effectively. And it isn't really THAT bad if you go 5 hours without slow or sleeping. What is bad is if you run around for 20 hours looking for someone or whatever and you haven't used slow or the sleeping technique. Also, always keep milk on hand and try to always be full. You want to maximize your mana regen with simple tools, not with a tool that is going to have drawbacks if you can help it.
Keeping slow up 100% of the time in my opinion is not a good idea and generally I wouldn't advise it. It will make you eat extra damage in fights vs melee. Against a caster/communer I would probably have it up at the start, but don't feel as though it is one of your "must-haves" It does help your mana regen but it also has several drawbacks.
My biggest piece of advice to anyone trying to play a battlemage is to just remember that you are NOT that complex of a class and you really do not need to overthink things. I read that someone said cancellation is a big help…I never even use the spell except when preparing to fight the Wight and I need to remove fly. I run around when fighting and when not fighting and I always have the ability to keep all my spells up. I never need to duck away in a hidden place to cancel everything and re-prep. When chasing someone that you have on the run….don't stop to put blur back up. Don't stop to put air shield back up. Chase with either sharpmetal if they can counter and murder if they cannot. Having one or two spells down will not be the end of you. Obviously if you are chasing them and sharpmetal/murder only to find out they pulled a quick one on you with nymph hearts/red staff/etc then you need to get away and put those couple spells back up or get away altogether.
Battlemages really rely on some of the most basic PK skills. Knowing when to stay in the fight, knowing when to get away from the fight. Like I said, I try to start my fights around 8am…by 11am I have a general idea of where the fight is headed. If dispel/sear hasn't put it into my advantage by then…I'm gone.
Just to reiterate…don't take my word as gold here, don't take anyone elses either. Battlemage is a class you really just need to find your comfort zone with when dealing with the mana issue and spell utility. And don't feel like you need to only fight around noon…I've won plenty of battles without sear as well. Keep in mind that you have one of the best disarm abilities in the game…use it wisely.