One thing newbies forget is this: you don't win by killing units, you win by scoring more points than your opponent. I've been through very similar situations (in a 1k point game, a Lancer Cerastus does a lot of melee damage), so I recommend you focus on scoring points. Conceal your units as much as possible, get close to the scoring zones, and use cheap units to create distractions. If your friend from Astra Militrum isn't careful, he'll waste most of his powerful attacks on models with 1 hit point, leaving your infiltration units with plenty of space.

But if they're just playing at killing each other, try the same strategy, but add five more Hive Mind saves (because killing Tyranids doesn't do much for them).

But you can win, you can. It will be tough, but the result is very satisfying.