You could start by taking a warphead to try and counter/negate some of his psychic tests more effectively than an army without a psyker could. Warpheads also have access to high AP attacks, the occasional zzap could prove handy.
What points is this? Because at the lower points, Hive Tyrants with wings or armour take up an awful lot of an army with regards to points. If there isnt much else you could kill everything else he has - focussing on the troops.
What I think is happening is that he takes an army that gives you the impression that assault-heavy ork tactics are required for victory. To be honest, I'd take a shooty-heavy army and pour shots at him. Taking 4+ troop choices is not difficult with orks, and if you spread them out accross the map his hive tyrant wont be able to eat all of them. I also find shoota boys quite effective against the weaker tyranids too (dont forget those 5 point upgrades to big shootas either!). If it's a higher points game, get 5 troops and just make sure they aren't bunched up so the tyrant doesn't have the turns to charge into all of them.
Tankbustas aren't bad against nids because there are no vehicles to distract them - they can always shoot at what you want. If they are in a protective wagon, they can keep a relatively safe distance. I'd consider a similar thing with lootas - perhaps even in a battlewagon if the points are high enough. Tyranids really struggle to penetrate heavy armour at ranged without a certain few units in the army - but I also find that armies that have a Tervigon and a tooled Hive Tyrant do not have the spare points to get said units without really lacking in other troop areas.
If you really want to focus fire down a Hive Tyrant, i'd consider rokkit buggies or rokkit koptas (rerolling to hit makes them better vs the flyers) or some zzap gun heavy weapon teams. It's fairly cheap to invest in these points wise (especially the zzaps) and for under 200 points you can have a considerable amount of anti-tyrantness. Personally I'd go with the koptas and buggies, target the tervigon and the rest of his troops, and then know i wont lose an objective's based game. (If it's a special mission where fast attack units can claim, focus on whatever flimsy fast attack he brought to. Knowing he has a Tyrant and a Tervigon, I'd guess he might have a unit of gargoyles at best.)
And most importantly, I'd build up a large horde of shoota boys. I find in this edition shootas are far more effective than sluggas against a larger amount of opposition types. Assaulting is extra dangerous these days and sometimes being able to sit back without getting hurt is extremely useful.
Hope this is helpful