How to drill a 0.75" hole in metal
For a hole of that size or larger a hole saw might be an easier method as it removes less material and may be more likely to stay centered due to its pilot bit.

However using the more standard bit you have is working and you should be able to get all the way through. The type of vibration and unevenness of the hole from that type of bit is not uncommon in my experience, and may not really matter in the end if the exact hole size does not need to be very precise.

While the bit might be dull, more likely it is harder to cut as you go deeper because initially more and more material has to be removed on each revolution, and also friction of the bit against the hole increases.

Tips:


Some lubrication (cutting oil - but in a pinch any oil may help) may stress the tools less
You can push hard but if you seem to stress the motor of your drill (you'll hear this) back off somewhat. Also pay attention to how hot the motor / casing is getting. Warm is OK but very hot or a burning smell is obviously going too far.
Be cautious as the bit starts to pass through the far side. Unique to drilling metal (as opposed to wood) the flutes of the bit may tend to "bite in" and you could get a sudden and significant wrenching action on your arm, hand, thumb, etc. Hold the drill very securely, use an extension handle if you have it, and maybe brace it with your body. For the last bit of depth I would push more lightly but spin the bit quite fast.
The hole may turn out to be a little smaller than 3/4" (or whatever exact size the bit really is, such as 47/64ths). That may seem impossible but if you think about what the cross-sectional shape of a slice of the bit looks like it may make more sense (its not a circle).
If the hole is rough you may need to file it down by hand before using it. Whatever goes through it is likely to get damaged.